OK I am considering using this mod but I'm trying to wrap my head around the fundamental things that it changes or adds.
It changes everything and nothing. May sound confusing, but I like to think that's what it does. It's still the same game, but everywhere I felt a mechanism needed to be reviewed or reinforced, I checked it out. Everywhere I felt the game needed fleshing, I fleshed it out. And what I didn't modify, other modders did (See OP credits section!). In that regard, XtraDeconstruct is an umbrella mod that gives you a chance to get the experience I wanted to have w/ LH. It also fixes numerous issues (Gremlins, as I like to call them) w/ LH.
Specifically, does it give cheats to the AI or simply improve their performance/strategy?
Both.
There's not a lot of games where the AI and the player play the same game and LH was never one of them (despite...). I did, however, increase the asymmetry between the AI and the player, gave the AI access to things it couldn't use (e.g. Cure Injuries, Curgen's Volcano, and many others), and generally simply made its decision-making process better (or so I like to think). It's never perfect and I still feel the AI fails to do what's best at times or even what I tell it to do, but I think it's better now than it was before. At the end of the day, however, I'm not a purist; I don't care how the AI ends up giving me a challenge as long as it does and as long as I feel its within what I expect from a Fantasy 4X TBS.
Does it add a lot of abilities to the current crop or are they more replacements for the ones that are there?
Both.
Hundreds of abilities have been added, but lots have also been replaced/modified.
Balance-wise, what is the mod aiming to achieve?
It makes the world harder, it makes the AI harder, but at the same time it gives the player the capacity to overcome this. But again, I feel compel to say balance in a strategy game is a chimera. You could have the best possible "balance" and then someone Curgen's Volcano an immobilized Sovereign. Or someone gets their hands on Curgen's Hammer. It's the nature of war and the nature of randomness. I'd rather think a game scales the challenges well enough to be enjoyable, pushes the limits of what one can do, and then lets the players decide on their own experience within that framework. That's what sandbox is to me and I hope my very own version of LH manages to do that. Whether this is only semantics, I don't know, but that's how I see it. That being said, much thoughts were put into balancing things (Ah!)...
Are the AIs fully capable of using the additional things given by the mod or are they hard-coded to use them rather than make decisions on what to do?
Both.
Depends on the specifics. And sometimes they just can't use the new things at all because XML doesn't give modders enough flexibility to let the AI take a good decision about something. e.g. There's no ValueCalcWrapper for Strategic Spells, which is a major limitation, to the extent that some Spells never made it in the mod or were toned down because the AI couldn't use them.
Does the AI no longer design its units but instead pull from a database of pre-designed units?
The AI never designed its own units. How it worked in Vanilla LH is the AI accesses the stock units, the played-designed units, and the AIOnly units (which are pulled from a database of pre-designed AIOnly units). In Xtra, the Vanilla AIOnly units have been scrapped in favor of new/enhanced AIOnly units. Otherwise, the AI has access to the stock units and the played-designed units as it did before.
How does it fit in with 2.0 now that it is live?
It's compatible? 
Stamina has been renamed Battle Wisdom. Abilities/Spells that require Battle Wisdom generally also have an added Cooldown (2, 3, 4, 5, 6, depends), so you can't accumulate Battle Wisdom indefinitely and chain cast these. Some of the new classes (Bard, Ninja, Ranger, Shaman) have access to a few new Battle Wisdom-based abilities, similar to what they added for Assassin, Commander, Defender, Mage, and Warrior. There's a few items making use of this as well. I'd say it's compatible, yeah.
If there is something else you think I should know before jumping in, please let me know what I should be aware of? Also, what are the devs thoughts on this mod in terms of how it changes the game if they've ever stated them?
It's probably better to remove your old custom Factions/Sovereigns (just move them outside of your LH folder), they wouldn't be playing with the same rules and would in fact be at quite a disadvantage. It's also possible to simply "upgrade" them by adding the new Tech Tree and the Deorcnysse fix. The Sovereigns would be a bit longer to fix, but also possible.
New Tech Tree. Your new Custom Factions will need to have that new Tech Tree modded in. It's explained in A_UserGuide.txt, section M1.
You will need to use a new set of .dxpack (User Interface) or you will have some issues. It's explained in A_UserGuide.txt . Either you can read section H1 and skip the rest of the H. sections, or read them all, or just read H9., which would be the minimum.
Speaking of A_UserGuide.txt , it's nightmarishly long, it's glorious; I try to make it longer w/ every iteration. Might be a fun read at work.
BTW, the emoticon you just saw, you can create it when you combine X and D. I like to think it's Stardock's tribute to XtraDeconstruct. !ba-dum ching!