Part (but by no means all) of the reason Taiwan doesn't claim to be an independent country separate from China is because China gets rather upset any time they suggest that, and the threat of military action is ever present.

Regarding your questions at the end, I'd guess around half the American population would agree with those things. (You might have to explain what happened with Hawaii first, I don't know how common knowledge of that history is.) Certainly it's by no means universal, but lots of Americans do acknowledge our past (and even present) sins.