1. Not sure about this one. The U.S. political situation allows them to declare war if UK is attacked by Japan, but I’m not sure if they can do this immediately or if they have to wait until their turn.
2. They would both defend together, yes.
3. The UK battleship would not defend as you have not declared war on UK. It would be able to withdraw on UK’s next turn.
4. ANZAC ships would defend because any declaration of war between Japan and UK automatically brings in ANZAC.
5. You would have to declare war on ANZAC to do this. You’re not allowed to place units in land territories occupied by a power you’re not at war with. You also must be at war with UK, and by extension ANZAC, to attack the Dutch territories.