Hi
i also suffer from tmj and had three of my wisdom teeth removed last week.
First of all, it is definitely a good idea to have general anaesthetic with tmj. I've had similar experiences to you at the dentist with just routine treatment so having wisdom teeth out under local anaesthetic is not a good bet! It's a good idea to let the surgeon and anaesthesiologist know you have tmj before the operation, but surgeons will be gentle with the way they position your jaw in theatre regardless.
I had a chat with my surgeon before the op about implications for my tmj. Clearly, the operation will cause it to flare up in the short term given the length of time the jaw is kept open during surgery, but your tmj should ease back to "normal" within a few weeks (one bad point is that you can't wear your splint at night for the first couple of weeks). The key point he emphasised is that the severity of pain/swelling is mainly determined by the specifics of the wisdom teeth themselves - so a heavily impacted wisdom tooth will cause more pain/swelling after the operation (as a general rule lower wisdom teeth tend to be worse than the upper teeth)
as yours have not fully erupted they may take a little longer to remove and lead to a bit more swelling than normal, but given you are quite young the roots of the teeth won't be very deep so should cause less stress to your jaw.
I had a good experience after the operation in that I was able to get normal movement back into my jaw within a week (although it was still a bit stiff and sore - similar to after having a filling, under local, at a dentist).
So just to sum up your quick q's:
1) severity of swelling is mainly down to the specific attributes of the wisdom tooth (how deep/impacted it is)
2) unfortunately it will a bit, in the short-term, given the length of time you have your mouth open in theatre. But this should calm down after a few weeks.
3) my swelling went down within a week, although your gums will inevitably still feel sore and a little swollen.
4) definitely - plus after they put you to sleep, they will inject your mouth local anaesthetic (as though you were having it done by your regular dentist) which means they do not have to put you asleep for too long so the effects of the general anaesthetic (and the immediate pain after the op) won't be so bad.
Hope this helps and let me know if you have any other queries!
Matt