Do you think the American government is able to defend Taiwan right now?

With China about 100 miles from Taiwan, I don't see how anyone could get close without mass casualties. China has the shorter and more secure supply lines. They could send an invasion force using numerous small water vessels in waters they could easily defend. In the end, the losing side would just destroy all the important places in Taiwan.

Would China actually bother with that? I don't think so. They like doing business with the Americans, and that would basically be a declaration of war to the USA. Even if it didn't boil down to that, sanctions would hurt them plenty, much more than they want. After all, Taiwan wasn't not for a split second part of Communist China, so what's the point of risking anything for an overcrowded island as long as no one recognizes them as independent?

So yes, I think the conflict will definitely remain frozen for the next decades, and it will be at least until either the CPC loses control of the mainland, the USA lose their grip on the region, or some US politician goes bananas and pushes for Taiwanese independence.

> they actually consider themselves to be the legitimate government of China

That's not the case since 1991.

Technically, they do, they are forced to remain the Republic of China (and also lay a claim on Mongolia) because any change of status would be interpreted by The PRC as a declaration of independence. So yes, while it's quite clear they don't care about the mainland, they have to de jure still keep the irredentist clauses in their laws and statutes in order to avoid war with the Chinese.