The way Team Aerial Combos work is that when you TAC and your character pops in their is no hit stun scaling while you are in the air...in other words if you could just in the air without landing you could bop a man forever and he'd never fall out unlike a normal air combo. Well as it turns out if you bust out an air move like Sentinel's air heavy right before you touch the ground and hold up afterwards there is a little jerk animation that happens when you jump that you dont see normally...what just happened is that the game caught the attack you threw out in the air connecting, but you jumped up before it caught on that you landed so it thinks you NEVER touched the ground. This means that once you get the timing down you can just hit these combos where you touch the ground while hitting a move right before you make contact so that you can pop back up and never let the combo end.
Amaterasu's is the easiest as its just hit H repeatedly. Some folks only have a TAC infinite depending on the direction they hit when they tried to tag in their partner for a team aerial combo. The whole thing is really bullshit though.
Snap in unblockable setups are basically someone setting up a combo that ends in a snap back to force in a character they want to kill. After the snap out they can call an assist to lock you down as you come in and some assists when paired with the right partner are unblockable and Touch of Death. You heard me...if they touch you once, they snap you out and hit the unblockable loop combo and when you die they do the same setup on your next two characters. Firebrand and Skrull are notorious for this...its part of the reason why so many folks started exploring the idea of making insane full screen zoning teams. If you want a solid starter team go with Zero/Dr. Doom/Vergil in that order. You have sougenmu +Doom bullet hell, Xfactor 3 Vergil as an anchor and Doom to lock folks down and do a ton of TAC infinites and loops with. Go ham...its all thats left.
This is why I dont think tag team matches in MK10 is something we should hope they emphasize improving. Its really hard to balance those games and its hard enough balancing normal MK. Really hope to see me some Tonya though. Im betting all the old crew returns though but under command of Quan Chi.