Gia’h having access to all the powers doesn’t mean she knows how to use them all effectively. Some may be too much of a strain on a body that didn’t obtain them naturally, there’s plenty of ways to write around that.

The US declaring war on all aliens is actually how the first SWORD miniseries at Marvel began so I assume that will be an adapted plot somewhere, plus it kind of feels fitting in a world where aliens have attacked Earth several times over and killed half the universe.