I largely agree with Speedkat's answer but had enough small comments and suggestions for fixes that I decided to post my own:
Expanded Spell List
This is a little too good at blast spells; the plain Warlock spell list has very few multitarget damage spells, and the patrons that grant blast spells generally fall into two categories:
- Highly themed/highly resisted: The Fiend gives a lot a fire blast spells, but they're all fire, and fire is the most resisted damage type
- Limited/delayed: Most other patrons that grant them only grant one option; and only at fifth level; e.g. Hexblade's Cone of Cold, Celestial's Flame strike.
The other three patrons grant none at all. Your patron is granting two (Lightning Bolt and Cone of Cold) with different (both less resisted) damage types, and granting one of them relatively early (5th level, vs. 9th level for all non-Fiend Warlocks).
Ignoring balance concerns, half of these theme spells are thematically appropriate to only one form of genie; while Absorb Elements is multi-elemental in focus, and Identify, Rope Trick, Remove Curse, Polymorph, and Creation are all non-elemental (and aside from Identify, I like them as "things genies can do", in particular imagining a themed Rope Trick that turns you to smoke and hides you in a lamp or something), the other four spells are really only appropriate to one type of Patron. Perhaps subdivide the bonus spells? One spell of each level that's unthemed, and then one spell of each level that is an option for that particular Patron (with no patron granting more than one blaster spell aside from possibly Efreeti, which could borrow Fiend fire spells). Efreeti patrons granting Cone of Cold is ridiculous on its face; grant fire/light/movement spells from them, air/flying/lightning/thunder (maybe illusion?) spells from Djinn, water/ice/acid/cold spells from Marid, and earth/acid/object manipulation spells from Dao (preemptive note: Unless the other Dao abilities are dialed back heavily, don't grant them Animate Object, which is one of the best fifth level spells on both versatility and damage output; on top of the other features, it would just make Dao the only choice anyone would ever make for this Patron).
Genie’s Lesser Wish
Starting at 1st level, you can invoke the power of your patron to
grant you a benefit, depending on the kind of Genie your pact is with:
- Djinn - As a reaction, add your warlock level to a saving throw that
you make.
- Efreeti - As a bonus action, add your warlock level in fire damage to
a spell or weapon attack roll.
- Marid - As a bonus action, add your warlock level to a skill check
- Dao - As a reaction to a creature being attacked, add your warlock
level to a that creature’s AC until the next round.
You may use the Genie’s Lesser Wish feature once per long rest.
For Efreeti, this is a little unclear: "add your warlock level in fire damage to a spell or weapon attack roll". Questions:
- Does it boost the attack roll, the damage, or both? (One weird reading would be boosting spell damage, while boosting weapon attack rolls)
- Must the spell be a fire spell, or is it adding fire damage regardless of spell's damage type?
- If not, must it be a spell that does damage? Can you damage someone with Hold Person?
- Must the spell require an attack roll, or does it work on spells that force saves?
- Does the bonus damage apply to a single damage roll on a single target, a single damage roll on all targets (much better for blast spells), or all damage rolls for a single attack (multi-ray eldritch blast gets even more ridiculous, but for a daily power that's fine)?
- For spells that require an attack roll, do you choose to invoke this power before attacking (spending the bonus action and the power without knowing if you hit), or is the bonus action/power spent reactively after you've hit?
That last question is important, since bounded accuracy means you'll usually only be hitting about half the time (usually slightly more than half the time, but not much), so the expected damage benefit from this feature is roughly halved if you might waste it.
In any event, for Efreeti, assuming it only boosts damage, not attack rolls, and especially since the damage type is fire, the power seems fine. A little weak at the early levels, and perhaps a bit odd depending on the answers to the other questions, but fine.
For all other Patrons, this is weak in the very early levels, too good at 6th level and beyond, and becomes broken not long after that. Virtually anything that grants bonuses to d20 success checks of any kind is naturally capped to a low value (either a stat modifier or your proficiency bonus, either of which narrows the range of the bonus to between +2 and +6 barring exceptional circumstances). The only exception I can think of is the War Cleric's level 2 Guided Strike Channel Divinity power, which grants a fixed +10, self only (becoming usable on allies at level 6). +10 is already insanely good, and since Clerics get relatively few class features, having one very good one is not unreasonable.
By contrast, your power is better (if used less often) than the War Cleric's for half the level progression (11-20), and it's just one of many powers Warlocks get between their Pact and their Patron.
It's also a little unclear why the Dao ability is self or other (and with no range limit), while the Djinn ability is self only (saves in general are less common than attacks against AC, so why make the AC defense more versatile?).
If you want something faintly balanced, limit the benefit of Djinn, Marid and Dao to +Cha. Maybe let it double the proficiency bonus for Marid rather than have it Cha-based, making it more like (and unstackable with, to limit dip potential) the various Expertise abilities.
Miraculous Protection
Starting at 6th level, you may use the Lesser Wish feature twice per
long rest. Also, you gain resistance to particular types of damage
associated with your patron:
- Djinn - Lightning & Thunder
- Efreeti - Fire & Radiant
- Marid - Acid & Cold
- Dao - Bludgeoning, Slashing, & Piercing
As others have noted, Dao is way too good, and too early for a benefit like that. If it were limited to resistance to bludgeoning/slashing/piercing from non-adamantine, non-magical weapon attacks, it would still be much better than the other options, and too early, but just barely on the edge of what's acceptable, but you'd need to make sure all the other Dao powers were worse than the other Genie powers (right now, Dao has the best suite of powers, by far). About the only mitigating factor here is that having a Genie patron means no Hexblade, so you're unlikely to be a frontline fighter (unless you really like MAD), limiting the amount of weapon damage you expect to encounter (assuming your tanks are doing their job).
Alternatively, find thematic non-weapon damage types for the Dao, or limit it to a single type of weapon damage. Cold and Poison maybe (granting advantage on saves vs. poison as well as normal), or just bludgeoning from non-adamantine, non-magical weapons.
Mystical Mobility
Starting at 10th level, you gain increased mobility, depending on the patron you have chosen:
- Djinn - You gain a flying speed of 15 feet.
- Efreeti - Your walking speed increases by 10 feet.
- Marid - You gain a swimming speed of 30 feet
- Dao - You gain a burrowing speed of 15 feet.
Aside from Dao, all of these are fine (Marid is pretty situational and not particularly special; I might add water-breathing to the power suite so it's at least fully usable in those situations). As others have noted, at-will burrowing speed is too good, as it's basically flying (immunity to attacks from many enemies) without the downsides (e.g. falling when immobilized). It's also granting immunity from opportunity attacks (because sinking five feet straight down doesn't take you out of the opponent's threat range, and when you do leave their range after that, you have total cover). In "the real world", the fact that you're blind while moving/between turns is a balancing factor (everything else with burrowing speed has tremorsense to compensate), but it's nigh impossible to adhere to this limitation without actually blindfolding the player between turns and only giving them seconds after the blindfold removal to let them declare actions to simulate how disorienting popping out of the ground for a moment over and over with no idea what's going on in between; if they have Ghostly Gaze, then they lose that weakness too (in exchange for losing their concentration slot and spending one in 10 actions renewing it).
A more balanced Dao power might be just the ability to ignore difficult terrain; weaker than flying, more situational, but the other Dao powers are already too good, so you want Dao weaker here.
Incredible Power
Starting at 14th level, you may use the Lesser Wish feature a number
of times equal to your Charisma modifier (minimum of 2 uses).
If Lesser Wish were less powerful (capped by stat modifier or proficiency bonus) this would be fine. As is, +14 to five rolls a day is insane.
Additionally, choose one of the resistances granted by Miraculous
Protection; that resistance is now an immunity.
Fine for all but Dao. For Dao, overpowered, even if it's limited to non-adamantine, non-magic weapon attacks (unlike previous editions, natural weapon attacks aren't magical unless explicitly specified to be so, so even at high levels, a lot of non-weapon using monsters are limited to one non-magical damage type, and immunity to that type means they can't hurt you at all). Reasonable if Dao is a pair of "elemental" resistances. If Dao is a single damage type resistance (bludgeoning), perhaps extend it to another (e.g. piercing) rather than granting immunity.
At 17th level, you may choose the Wish spell as your 9th level
Mystic Arcanum.
While late level benefits are usually good, this is probably too good. Wish is the best spell in the game, based solely on its "safe" usage (mimicking any spell below 9th level on demand, without using material components, with a one action casting time). Only two classes in the game have it on their list (Sorcerer and Wizard), and only two others have access at all (Bard via Magical Secrets, Arcana domain clerics via Arcane Mastery). In all cases, it's for classes that are thematically focused on maximum spellcasting knowledge and flexibility; Warlock is thematically quite narrowly focused, with single-target power, but little knowledge/flexibility (with the highly limited spell list reflecting this; see complete lack of blast spells mentioned earlier, as well as very few multitarget or utility/creation-y spells). Their Mystic Arcanum are even more limited; you only ever know one spell of each level, from the already highly restrictive Warlock spell list. Giving them Wish blows that out of the water; now they can use high level spells from any class, bypassing the thematic (and balance) restrictions applied to the Warlock spell list. Sure, Wish bypasses thematic limits for the other classes that get it (Wizards/Sorcerer can heal, Bards/Clerics can blast better, etc.), but those other classes were still pretty flexible before; Warlock isn't, on purpose.
