Air units can indeed attack subs. Basically, any unit can hit any other unit, unless the rules say they can't. For example, the rules specifically say that subs can't hit planes, and that land units can't hit sea units.
If there are no attacking destroyers, the surviving defending subs can submerge at the end of the first round of combat. They do have to survive that one round of attacks, though.
This is all explained (indirectly) in the rules in the combat section and the destroyer and sub unit profiles. Your question is also directly addressed by the FAQ