Question

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)

Morning  Bigtasty. Air units can always attack  Ground units and can cease attacking at the attacker’s choice;  they just can’t capture the territory.

No. In an amphibious assault, Cruisers and Battleships can hit any unit on the territory being invaded. They only get one round of attacks and only one ship can fire for each amphibiously attacking Ground unit.
But: the ships cannot be hit by the defenders. The defenders do get to shoot back, simultaneously, at the landing units. The defenders can even hit Air units.
I hope that helps.

To clarify:

@Bigtasty:

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.

You must understand that land units are not defenseless against air units.  They can hit them.  Any unit can hit any other unit unless the rules specifically say it can’t (subs can’t hit air units, for example).

@Bigtasty:

Also can battleships/cruisers only attack land units during amphibious assaults?

They may not attack land units in any other circumstance.

@Bigtasty:

Ok just want to make sure I understand this 100%. If a land unit such as a tank or infantry is attacked by an airplane, it can return fire as if it were being attacked by other land units?

Yes!