Yes, once the DD is destroyed the planes can no longer hit the Subs so the battle would end.
And yes, since subs can never hit planes any sub hits go to fleet elements.
I guess this would form a partial exception to the “transports die last” rule. For instance if two DDs, three fighters, and a transport attack 3 subs, and on the first round the subs get three hits, the transport would be sunk even though the fighters are still alive, since that third sub hit could only be resolved on a sea unit.
