Can you upgrade the hardware in a MacBook Air 2012

Nope - the macbook air is a single integrated unit under the hood. Nothing is user upgradeable (at least not practically or without a lot of desoldering/soldering and major electronic surgery).

Since the device is not user upgradeable, you will have to scoure the internet for the specifics of the logicboard, chipsets used and so on to figure out compatability and what would or would not work. That is not general knowledge information, so you'll have to search and find it all yourself. I'd also wager you'll end up spending as much or even more moeny than a new machine would be.

Honestly, to me, it would not be even remotely worth the effort. Sell the current MBA and buy what you really want or need. If PC gaming is really your big thing, I would honestly suggest getting a Windows native PC and not an Apple product in the first place (you'll get better gaming experience for less money).

It is, effectively, impossible. The GPU is part of the processor, there is not a separate dedicated GPU in the Air. Unless you have the equipment necessary to desolder hundreds of contact points simultaneously in order to remove the CPU, you would not be able to even remove the chip. I haven't looked too much into this, but I believe Haswell also uses a different socket (I could be wrong on that though). I would point out that I have NEVER heard of this being done.