Yes, an act of war by Japan on UK or ANZAC(and maybe France?) puts them at war with the US.
It does not put them at war. It allows them to declare war. There is a rather large distinction, as Japan can end the turn in seazones with US ships (or attack seazones with both US and UK/Anzac ships, ignoring the US ships) that are still friendly to them until the US declares war on the combat move of its next turn.
Japan declaring war on France has no impact whatsoever. Japan can declare war on france and as long as they don’t attack FIC, they’ll continue to collect their National Objective. Even if they do attack FIC, japan only loses their objective. It does not permit the US to declare war.