They are there as a deadman’s switch, so if China invades Taiwan, America will have to get involved. They had the same play on the Korean border for a few decades. You are correct it isn’t just training, but to ensure the American people are committed because American troops would have been killed in the PLA’s initial missile volley.

That's an escalation. It also violates the sovereignty of China, which America recognizes officially under the "one china policy".

That’s international politics. Yes, mainland Chinese will be face hurt, but face hurt is not against Geneva convention.

The Taiwan situation has been escalating for awhile now that almost everyone expects an invasion before Xi’s lifetime term ends.