That can be more complicated, based on what I heard about i.e. Guantanamo Bay, where technically the Cuban goverment would really like the USA army to leave, and USA pretends they have a lease and that everything is fine.
I am not sure if there are other examples, though.
Well, the previous Cuban government gave the US permission for the base at Guantanamo Bay. Then the Cuban Revolution happened. The US does not have permission from the current Cuban government, but is holding it to the agreements made by its predecessor.
The USA hasn't tried to annex parts of those countries.
> the UK going to war with the "neighbouring" Falkland Islands
Most countries would fight a war if their territory was invaded.