The class is in parts half-baked (so-to-speak), but not overpowered according to my evaluation.
It seems to me that the author knows several of the design principles that are present in official subclasses. However, there are also a few occasions where either the balancing is off or the phrasing deviates from the "standard".
What's less good:
- Spell slot progression: it should match how fast other half-casters (paladins, normal rangers) get spell slots. It mostly matches those, but this class gains their respective highest-level slots at other times than normal half-caster classes (compare slots at for example character levels 9, 14-16 and 18-20).
- Hunter Senses: this class doesn't have favored enemies. Bad copy and paste ^^
- Some Ranger Styles are unbalanced:
- Battle Movement: should only apply to melee attacks. Probably an oversight.
- Enhanced Hunter's Mark: this is basically free damage, and not insignificant amounts. If the feature required you to hit (not attack) both targets, it would be much more balanced. Requiring the use of a bonus action to deal the damage would probably also be a good idea, though I haven't tested either of these changes in a game.
- Battle Attacker Master: aside from the strange name, this is by far the most powerful Ranger Style. Any reasonable ranger player would choose this feature without a second thought; in other words, this would be better as its own class feature, not a Ranger Style (simultaneously reducing the number of total styles to 6, which would allow you to conveniently match their number with the proficiency bonus, removing the need for a separate counter). That being said, it's also phrased strangely ("ability to attack 3 times a turn"). The expected phrasing would be "when you take the Attack action, you can attack three times".
- Resilient Body: seems very strong at first, but for comparison: a Paladin's Lay on Hands can heal any character(s) for a guaranteed total of 100 hit points, not just yourself for a random 4-80HP. It's certainly a strong feature, but I don't think it's too broken (if not combined with the other unbalanced features mentioned above).
If these features were to be changed, the class would be pretty balanced, I think. It could be on the strong side, but there are no features that strong enough for me to take this class without a second thought if my goal was to make the mechanically strongest possible character.
The potential problems you mentioned are not really problems, in my opinion. Compare them with normal classes for reference:
- Expertise at level 3: bards gain 2x expertise at level 3 and another 2x at level 10, while rogues gain 2x expertise at level 1 and another 2x at level 6. Thus, three expertise skills at level 3 is unusual, but not broken, in my opinion. I believe there are also (regular or racial) feats that grant you expertise, so a variant human rogue would already have 3x expertise at level 1. Either way, expertise is useful out of combat, but because it's usually not relevant during combat, it's not a huge balancing issue anyway.
- 120 feet darkvision: not a problem, Drow get this as a "level 0" racial feature, and Warlocks can get an even better (because it works in magical darkness) 120 feet Devil's Sight. There are also some other features that add +30 to your darkvision (though I can't remember right now how to get them). Either way, it doesn't make much of a difference whether you have 120, 150, or 180 feet darkvision range. Most of the time, your enemies won't be that far away - 5e is not designed for such long-range combat, even if a longbow, for example, can theoretically shoot that far.
- Underdark favored terrain: not a problem either (same as with 120 feet darkvision). Poison resistance and another language are certainly useful, but Dwarves, Stout halflings, or certain Dragonborn get this at "level 0", while level 10 druids are outright immune to poison. If anything, the Desert terrain is a little strong (IIRC, fire is the most common damage type in 5e), but I don't think it's too unbalanced, either.
- Distance strike: if I read this right, you have to spend a bonus action once (!) to gain a permanent +1d8/+2d8 against a creature, and there is no restriction against applying this to multiple creatures. To be balanced, it should work only once, so you have to spend a BA each time.
- Spectral defense: not a huge problem, but this probably shouldn't have unlimited uses (maybe uses = WIS modifier or something like that).
- Unseen: this is pretty strong. The bonus damage is thankfully limited, but it's still pretty significant, and the +d6 to hit (on top of advantage if the target can't see you!) is way too strong. If paired with 2 levels of Warlock for the Devil's Sight invocation (see through magical darkness) and maybe the Drow race for a free casting of Darkness, this makes a pretty strong combo. It's also lacking a "you regain all expended features on a short/long rest" phrase.
- Stalker's Flurry: pretty strong as well, could probably use a limit of some kind.
- Frozen Cover: another free, permanent +2d4 damage. It's too much, I'd dump this feature entirely or tune it down to something weaker at the very least.
- Enchanted Frost Arrow: no way for the creature to escape being stunned. This is a save-or-die feature and as such should be burned at the stake. It needs a limit (maybe 1 minute) and should allow the creature to repeat the save each turn. And, again, this feature should not be unlimited.
Overall, the base class isn't too bad if you apply a few fixes, but if paired with the subclasses, you can stack your bonus damage on attacks insanely high.
Example (for ranged attacks made by a level 18+ ranger):
- Urban favored terrain: ignore half or three-quarters cover
- Archery fighting style: +2 to attack roll
- Hunter's mark: +1d12 (at level 17+) to damage roll, unlimited times per turn
- Extra Attack: 2 attacks per turn (not unbalanced by itself)
- Enhanced Hunters Mark: as long as you have two enemies, this is a free +2d10 psychic damage to both targets.
- Battle Attacker Master: 3 attacks per Attack action (even though the feature phrases it strangely)
- Gloom Stalker subclass: attack from darkness for advantage against creatures that can't see you, with an additional +1d6 to attacks, and sometimes also +2d6 damage (limited uses).
When attacking from darkness, this is a grand total of +1d6+2 to attack rolls with advantage, with a damage bonus of +1d12+2d10 against two targets.
Assuming no magical equipment (such as +1 or better weapons), this adds up with +5 DEX and +6 proficiency bonus to an average to-hit-bonus of +16.5 (plus advantage!), and an average damage bonus of +22.5. With three attacks per turn (one of which only gets a damage bonus of +11.5) and when using a longbow, this totals 2x1d8+22.5+1d8+11.5 = 47.5 average damage each turn, all of which you can deal from 150 feet away, or from 600 feet away if you're willing to give up your advantage.
If you combine this with the Collateral Ranger Style it's even more insane; and since you have advantage and such a high attack bonus, it's pretty likely for you to hit the secondary and tertiary targets.