Different Alternating Possession Questions

[sjhoops]

HS Rules-
1. Team A receives ball after AP. While Team A is throwing in ball, Team B intercepts throw in. Arrow stays with Team A for the next AP?

2. Team A receives ball after AP with 1 or 2 seconds left in Period. To keep posession for the start of the next period, they either a) pass it directly to Team B-see above- b) throw it out of bounds with no one touching it or c) Fumble it out of bounds with out having possession at a more desirable place on the court. Would they receive the Ball Back to start the next period in all of these cases?