1: the AP is trying to maintain the attitude that the aircraft was in when you last released the trimmer button, subject to the channels you have selected. If you only have AP heading selected and you release the trimmer in a bank, it'll only try to keep the nose pointed in the same (compass) direction. It won't try to maintain the bank or pitch.
2: Flight director is damping only. If you press the trimmer button, when you release it you will get HUD indications telling you what attitude the AP would be trying to achieve if you had it engaged.
3: There are different schools of thought on this. I find it easier to just hold down the trim every time I move the cyclic, but others prefer to repeatedly tap the trim button during manoeuvres, which apparently is what the real pilots do.