A fear and death class focused on using death and the fear that comes with it to its advantage as both a caster and martial class.

Here's your challenge question: What about your concept can't be filled by a Death cleric, Undead warlock, Conquest paladin, or Oathbreaker paladin with the numbers filed off? What makes an Undertaker unique enough in theme or class fantasy (not mechanics!) that it needs a whole separate class?

A More Thorough Approach: needs focus, and then revision.

This is clunky in some places, confusing in others, and trying to do too many things at once. Some features seem left over from previous revisions as they mention things that are not present elsewhere in the class. The Aspects system is a mess with hints of gold and needs a lot of tightening up.

Does it meet the goals of the concept?:

• As a class invested in death and fear, yes but not well: most features are reasonably thematic but also messy and confusing. Your core concept could use additional focus, and from there key abilities also need revision to be less confusing.
• As accommodating both a caster-playstyle and a martial-playstyle? No, and the attempts to do both make this messier.
• I'm not entirely sure about established power levels. In terms of established progression patterns, it fails. It currently is too front-loaded and puts common features at the wrong levels. The new unique features are messy and arguably weak due to overly-stringent activation requirements; retooled versions of existing features pulled from elsewhere have received tweaks that make them worse.

How do your design choices reinforce your intended concept?

IMO, good class/subclass design usually has a central core concept, and each class feature comes back to that concept directly. From my own experience, the homebrew cleric subclass for Tiamat I asked for review for--everything derives from the central concept of "Tiamat is warlike and terrifying, and all chromatic dragons at once, so all features must also represent some part of that combination in some way".

When you want to include something, you should check it against the core concept. Is it on theme? Are you introducing a new angle to the core theme, and if so, how are you tying other class features in to reinforce that this is thematic instead of tacked on?

For example, your central concept as you've stated in the question is this:

What does it do: A fear and death class focused on using death and the fear that comes with it to its advantage as both a caster and martial class.

You don't mention wiping out undead anywhere; where are Sense the Dead and Hatred of the Dead coming from, then? Sure, worshipers of true death often hate that which tries to subvert it, but these are also the only features that ever mention undead at all, and are therefore out of place.

Again, I find your central concept fuzzy. "A fear and death class focused on using death and the fear that comes with it to its advantage as both a caster and martial class." Published options for this already exist in a couple of flavors. What about the Undertaker makes it unique? Put that in your core concept statement to remind yourself and let it be a guidepost for further revisions.

Too Much Information!

You have a lot of features here, to the point where there's arguably too much to keep track of.

• Some features may just be overloading the class with too much to remember, or may be insufficiently on-concept, and can be cut outright.
• Some features are listed each time you get a new use in the class' progression. This is OK in the table, since additional picks/uses can stand alone as a new level's benefit (e.g., Sorcerer's Metamagic or Cleric's Channel Divinity), but in the list of features it can be summarized at the end of the main feature block as "you gain additional picks/uses at levels X, Y, and Z". Improved Aspect is the main offender here.
• Some features have too many parts, not all of which are cohesive. Some of those can be split apart into disparate parts, which might be full features in and of themselves. See Gaze of the Dead.

Rule of Thumb #1: if you introduce additional parts in the same feature, all parts of the feature should relate to each other, or at least relate to the concept as described by the name of the feature. If you have two parts to a feature and they're doing very different things, then those parts should be split up into separate features. Help the player remember their own abilities by grouping said abilities logically.

Too Front-Loaded!

Look at your class progression table. How many features do you get in the first 6 levels? How many dead levels do you have, and where are they?

Even if you disagree with me that there are too many features overall, you're handing them out too quickly. Level 6, for example, has three different completely new features, which is more than published material. The few instances where there are three features granted at a given level (Bard 10, Cleric 8), generally only one is a completely new feature, with the others being various upgrades on a preexisting feature or a regular ASI.

Several features you have at higher levels also aren't strong enough for their placement, or the published feature you're borrowing from comes earlier in the level progression. If you adjust accordingly (and I generally think you should), this compounds further.

Some things that are improvements on core class features, like Improved Aspects and Improved Transformation, could likely benefit from being retooled to a higher power tier and being pushed back to the middle levels of class progression. You have four dead levels (levels where the class gets nothing new): 7, 11, 14, and 18. You can, and should, move features around for an even spread across all 20 levels.

That's not the right level for that

You used some common class features but they're being introduced out of sync with where published material establishes they should go. Move them back to the established levels, and move the other new abilities around from there.

• Extra Attack should be at level 5, not 8.
• Cantrips should be included with Spellcasting at 3, instead of separate at 6.
• Reaper Transformation, which is a reskinned Form of Dread from Undead warlock, should come at 1, not 3.
• Dead Touched, a lightly tweaked version of Undead warlock's Grave Touched, should come at roughly level 6 where that subclass puts it, instead of 15.
• Dreadful Appearance, as a cosmetic feature, should not be a class progression feature at all. See: Xanathar's Guide to Everything, warlock or sorcerer optional roll tables for visible signs of your pact/heritage.

Weapons or spells?

You state this is a fear-and-death based class, and you want it to function both as caster and as martial. Nothing published does both simultaneously, but what about either?

The features you've pulled from existing material--specifically spell slot progression, Fighting Style, and Extra Attack--tell me, a hypothetical prospective player, that the intended combat role is predominantly going to revolve around weapon attacks with some support spellcasting on top. Reaper Transformation reinforces this, since at base level it works with weapon attacks but not spellcasting. This is comparable to an Eldritch Knight with some warlock flavor via Aspects.

This does not accommodate a caster playstyle, which by my understanding relies almost exclusively on spells and cantrips, and really wants full spellcasting progression to keep pace. And, if you leave those features in the base class, it shouldn't. Classes make tradeoffs in design, and no one class can be everything all at once. Even warlock, which comes closest to being the most modular, specifically makes the player make mutually exclusive choices that steer them towards either a more weapon- or spells-focused style. It still doesn't do both at once very well, its spellcasting progression is unique and limited, and arguably it never reaches the same level of caster as regular full casters, even when tooled that way.

You have a decision to make here: either embrace what you've already written and have the class be a magically-augmented martial class like Eldritch Knight, or invest in a much more comprehensive redesign to more effectively offer a player the choice of weapon vs spell.

Trying to balance increased power with increased risk or drawback is a trap

Darth Pseudonym said it better than I could here; trying to balance a powerful feature by adding an equal-but-opposite drawback doesn't balance the feature, it just breaks it in a different direction too.

Warrior of Magic and Metal compares with Bladesinger's Extra Attack and Eldritch Knight's War Magic, but you can burn your own lifeforce to make the cantrip the bonus action for 2 weapon attacks in the main action. You can also use 1st level spells.

Rule of Thumb #2: your bounds for balance are what has been officially published. If you find that a feature is demonstrably better than the central mechanic of a published class, redesign it. High level spellcasting is a frequent target for this; if you have more high-level spells or get them earlier than a wizard/cleric/druid, then you need to redesign that feature.

In this case, existing features allowing a class to mix weapon attacks and spellcasting only use cantrips; using 1st level spells goes over that, and the drawback does not balance it. This would work perfectly fine using the published feature as-is.

Blessing or Curse is generally just bad, as I note below in the features section, but in this case, the reduction in max hp and the potential for a curse also run afoul of this principle.

Reducing max hp is dangerous, especially for a lightly-armored weapon fighter. Why are you willingly weakening your own survivability? The curse possibilities are also dangerous, and several make you a load on your party if you're unlucky enough to get that one (looking at unconscious in particular).

Aspects

These get a whole section because they are a whole problem. Aspects are a mess that don't know what they are and therefore I don't know either.

Aspects want to be the backbone of this class; introduced early, you learn multiple of them, you can channel them to greater combat effect, and they get easier to use and stack as you gain levels in the class. I don't know that they're properly calibrated to actually be said backbone, though--some seem too complex to juggle multiple aspects active at once, others seem like too minor of a change in mechanics to justify.

On a more mechanical level, activating Aspects and maintaining multiple active aspects is a confusing mess.

• What's the baseline duration of an activated aspect? Everything has a default duration, especially if it takes concentration.
• You have multiple other features whose central benefit is "you no longer need to concentrate on your aspects"--are you sure this feature really needs concentration? Especially since a decent chunk of your spells list also requires concentration, which would make it mutually exclusive with this feature. Consider removing that requirement and expectation and see how that opens up more interesting options for making the core feature better.
• Having to concentration check every turn or lose your ability once again falls into the "I'll balance this power with extra drawbacks and risk" trap that I mentioned above is bad design.
• The levels at which you learn new aspects and improved aspects are uneven and could use reconfiguring to make progression more even across the board.
• Action cost to activate is costly in combat, and makes this weaker than similar class features that can be triggered on a bonus action.
• Each separate Aspect gets more potent at its own rate. Consider designating a level at which all basic aspects improve, like Arcane Archer's Arcane Shot options.

My recommendation is to refer you to the homebrew Star Wars 5e system, since the Sentinel class has a similar mechanic in its Ideals. When you take an Ideal, you gain a passive benefit, and then you have a limited pool of 'Ideal Manifestations' per long rest, which gives you an additional active benefit for a limited duration.

Tighten up what it means to know an aspect and to activate it; this may (likely will) require an overhaul of the Aspect effects.

Improved Aspect as-is is too weak; a lot of what it exists to mitigate I recommend removing from the base feature in order to make that one better and tighter to play. You have an interesting idea about picking certain Aspects to deepen your connection to, so what else might that look like? If you like what SW5e does with Ideals, consider adding a third thematic ability, at a higher power level and usable once per long rest, to each Aspect that becomes available when you pick it as an Improved Aspect. Just keep Rule of Thumb #2 in mind and mind how you set your prerequisites.

This is a good candidate for improving the feature power level and moving Improved Aspects picks to higher levels to balance the bulk of low-level features. One note here: move the final Improved Aspect up before level 20. A class capstone never shares its spotlight.

Features Breakdown

• Hit Dice, Equipment, Proficiencies: All fine for the most part. The specific combination of weapon and armor proficiencies imply a dexterity-based weapon fighter who uses finesse weaponry predominantly. Equipment doesn't quite match that expectation, and as a player I'd be trading up to a rapier or dual shortswords as soon as I could afford it. There's also no ranged or thrown option--the only classes that don't even get the option for something ranged in starter equipment are the ones that start with cantrips, so consider adding one in.

• Sense the Dead: Weaker compared to Divine Sense, and arguably off-theme, considering very little in this class makes mention of the undead at all. On the other hand, being able to sense where true death is being shirked could be a reasonable ability. I still recommend cutting to reduce overall features load unless you intend to emphasize undead in some fashion.

• Aspects: (See Aspects section above, significant rework needed). I also recommend moving this to level 2, where I kept thinking it was already at. Reference point: Eldritch Invocations.

• Fighting Style: Fine, but your starting equipment and available styles don't match. You can start with two light weapons but no ranged weapons, yet you can select Archery as a style but not Two-Weapon Fighting. Make them match, and you'll be fine.

• Spellcasting: Also fine. I recommend adding in toll the dead to the class list for thematic reasons. You may want to adjust the spells list for more variety, and even out the spells known progression.

• Reaper Transformation: is just Undead warlock's Form of Dread, and I think that's OK, actually. In fact, I think you should just rename the warlock feature and keep using it without further changes; see previous comments in Aspects section about removing the concentration requirement for Aspect activation.

  • I also think this should move to 1st level as per the warlock ability, and that the wording about channeling an aspect to create it should be removed as the feature on its own doesn't actually interact with the aspects aside from the concentration element. Let the general death transformation lead to embracing specific aspects of death in greater depth instead of the other way around.

• ASI/Feat: Standard progression at 4/8/12/16/19. Fine.

• Improved Aspect: See Aspects section above; likely to need significant rework based on rework of baseline Aspects. Depending on result, may come online at later level. Do consolidate all instances of picking a new Improved Aspect into the initial feature text, though; "You select additional Improved aspects at levels X and Y" should cover it.

• Dreadful Appearance: This isn't even a ribbon ability, this is purely cosmetic. Remove entirely from class progression and make a roll table at level 1 for added flavor.

• Cantrips: Why have these been separated out from Spellcasting? Put them back with it at level 3 like every other published class with cantrips.

• Warrior of Magic and Metal: Eldritch Knight's War Magic run through a Blood Maledict filter. I see what you're going for, but just use War Magic under a different name. Trying to add in 1st level spells makes it demonstrably better than published options trying to do the same thing, which trips Rule of Thumb #2.

• Hatred of the Dead: I think I spot a vestigial feature from a previous revision--was this previously a paladin subclass homebrew? "[...] due to you following the rules of the undertaker’s oath, [...]" There is no oath in this class. Considering that most references to undead have been stripped out, I think you can cut this entirely. It doesn't play into the central stated theme and you already have a lot going on in the lower levels.

• Improved Transformation: This is weak as-is. The additional temp hp is minimal at this level, and the additional triggers of "Spell attacks" doesn't do much at all--not many of your spells have spell attacks! Most rely on saving throws. Reconsider what sort of improvement you want this to have as you hit upper Tier 2 and going on into Tiers 3 and 4.

  • Also I recommend moving this off of level 8. ASI/Feat levels generally don't also have other new class features coming online at the same time.

• Extra Attack: Wrong level, move it back to level 5 as per established pattern. Otherwise fine.

• Death Can Have Me When It Earns Me: a 1/day, self-only, limited Bardic Inspiration. Better than the bard has at this level, but pretty weak overall. I recommend cutting it, and letting other features fill in.

  • This feels off-concept in a way I can't quite get into words; for a class based around embracing death for power and inspiring fear in others, how does this fit? Why does reveling in causing death grant you additional insight into survival or tough situations? As-written this class is more about causing lots of death than surviving or gaining wisdom from it.

• Prostrate Yourself: Evocative and thematic, but way too strong as-written, and missing pieces.

  • What's the DC of the Intimidate check? Are you trying to beat your own spell save DC? Consider having the target make a saving throw instead.
  • This might be left over from a previous paladin homebrew; is this referencing the Conquest paladin's 15th level feature Scornful Rebuke? If so, then borrow that feature under a different name and leave the additional conditions off of it. The higher levels of the class could use good features, so a reskinned Scornful Rebuke could be a natural fit for level 15.
  • Alternately, see Pyromancer sorcerer (UA) 14th level Pyromancer's Fury, which costs a reaction and does more damage. If you want to keep the conditions in, consider using a reaction trigger to inflict the combined damage/condition saving throw.

• Dead Touched: A lightly tweaked version of the Undead warlock's Grave Touched, and so too weak for 15th level. Move it back to roughly 6th level, where the original version is.

• Gaze of the Dead: This can be split into two separate abilities: the forced reroll, and the at-will speak with dead. Either piece is too weak for level 16; other published features can grant a better-controlled reroll at earlier levels (see: Lucky feat, Divination wizard's Portent).

  • Reference: Whispers of the Dead Invocation (level 9) for speak with dead feature.

• Blessing or Curse: This is bad. It is clunky and unintuitive to use, doesn't make sense why it skips over 5th or 6th level spells, and the attempt at offsetting increased power with high risk falls afoul of a common design trap that just breaks it again in a different direction.

  • If a feature risks removing you from playing, it's a bad feature. That's what your curse mechanic here does; if you're unlucky enough to be unconscious and nobody has the specific right spell to undo it, then you just don't get to play. Other options leave you a liability to your team if you get into trouble.
  • You are also relying on the player wanting to engage with the risky aspects as a way to control the feature's power. What if you just...don't use the feature unless it's safe to do so? Then it's a waste of a high-power class feature on the days you don't use it AND overly powerful on the days when you do because you've rested.
  • You run afoul of Rule of Thumb #2 here; as-written you can squeeze three level 7 spells out of this feature, which is more than wizards/clerics get at level 20.
  • Cut this entirely and find something else to come online at this spot. I recommend this level being the final choice of Aspect (See: warlock 18, when you get your last Invocation but nothing else).

• Lord of the Dead is mostly fine as a capstone! It clearly references paladin Oath transformations, so make the duration 1 minute instead of 3. You should also revisit those Aspects benefits after you've redesigned the Aspects system.

Some Housekeeping:

• This needs a language and formatting cleanup to bring it into line with published material.
• The class progression table needs to have the ASIs for 8th and 19th level added in to reflect 5e base standard (as well as stated ASI opportunities in class breakdown)
• Some features use Proficiency bonus as per-rest uses limit, some use WIS modifier. Consider picking one to use for all limited features.

And a possible editing tip for your next major revision:

A writer I respect once mentioned that her editing process, when she finished the first draft and moved onto the next, involved printing out the entire thing and then retyping it as she went. She found it much easier to catch errors that way. I think this could benefit from a clean run like that to catch where you have features that refer to something that no longer exists.

Also, try writing out a new progression table listing every time the class grants a new feature, an otherwise-unlisted upgrade to an existing feature, or additional uses of a feature; you should be able to see more clearly where there are too many things on a given level vs gaps to fill, and can rearrange features (and from there adjust power levels) where necessary. Every level should give something, even if that's just a new Aspect or a new pick for Improved Aspect; it's also OK for those to stand on their own.