Shooter from Team A is fouled as time expires with his team down 2. Lane cleared, no time left, ready for FTs. Team B requests time out. Does they get it? After searching for this one, I believe he does, but I still have some doubts....

Yes, Team B can be granted a timeout. Any further requests, from either Team A or Team B, are not granted.

Assuming the foul was during a 2-point attempt, if A1 misses the 1st shot, the 2nd is not attempted.