In the case of an all airplane attack, with fighter bombers or both, can they continue to attack a territory with no air cover or AA until all the defenders are dead or must they stop.
Attacking units (regardless of the type of unit) continue in attacking as long as you (the attacker) wish.
After the step of combat movement the step of combat follows up. “Combat” consists of “attacks” in territories or sea zones. Any attack in a territory or a seazone consists of “rounds” (one round=attacker rolls dice first, then defender rolls dice). When a round ends, the attacker -and only the attacker- decides to continue (next round starts) or to retreat. Translated into the case you mentioned: you -the attacker- attack (in this case with airplanes only) in a territory. After the first round (you roll dice, the defender rolls dice) you can decide to continue the attack or to retreat. This continues as long as you have units which can attack or the defender is dead or you retreat.
Also can battleships/cruisers only attack land units during amphibious assaults?
The question can be misread and I have to answer two ways:
Battleships and cruisers are the only vessels which can attack during amph. assault.
when they attack, they can attack any unit in the territory but they’ve got only one shot per landed unit. Example:
2 land units from a transport are landing, 1 battle ship (BB) and 2 cruiser are supporting the amph. assault.
two shots can be fired upon defending units, you can decide which ships fire (of cause you decide, that the BB and one of the cruisers should fire)