welcome to the forums!
1. Can you fly air units over enemy sea and land territories without AA during noncombat?
yes. you can always fly air over whatever you want so long as the air units can land. you could also fly air units over AA during noncombat too, but the AA gets to shoot at you depending on which version of the rules you are playing.
2. If an attacker fails to take an occupied enemy territory and the attack is over, can he then go back into that same territory with other units during the same combat move?
no. all combat moves are considered to take place at the same time, and, one you’ve started rolling, you can’t go back and make another combat move.