The US would never invade China, it would attempt to stand off and bomb China to degrade their military capabilities and economy (manufacturing in particular), along with fighting a naval war to try to determine naval supremacy around Asia. There would be some island battles between the two, to deny/seize territory. The conflict would be near-China and would involve China trying to deny the US the ability to operate effectively close to their territory. Right now the US can project across much of Asia, China can't project across the Pacific (or very far from their borders), so the conflict would largely happen in and around Asia. It would be a question of naval battles around Asia (and some limited conflict in the Pacific), denying the US Air Force the ability to bomb China, intermediate and medium range missiles (ship killers etc), and air defenses. The way things would go with North Korea, South Korea and Japan, would be of particular interest; as well as NATO; North Korea would go to war with South Korea if any serious conflict breaks out between the US and China. Russia would supply and intel-assist China as requested but not get involved directly. There is almost no scenario where Germany (and probably France as well) would join on to fighting a war against China over Taiwan; many NATO countries would refuse to get involved, which would end the NATO alliance. And if China decided to bomb eg Tokyo, they could obviously cause enormous destruction very easily, which presents Japan with a very difficult choice. There is a good reason nobody wants to see any of this happen.
If China were losing badly enough, they'd throw the nuclear card on the table. It presents a difficult scenario overall, as China can always draw a stalemate by using that whenever convenient: stop or I'll use nukes; it's the ultimate homefield advantage. If you're winning away from your home turf, and you're under threat of being nuked, your population will never support pressing forward (it would never be worth it, gain a bit of foreign land temporarily and lose your cities).