If we aren’t already in a world war from China solving Taiwan as you say, we would be in one from China taking Korea or Japan.
Taiwan just the last remnant that the losing faction of the China civil war still holds. I don't think that China wants to conquer korea or japan. Having a vassal is usually cheaper than outright conquest and occupation. They just want the US vassals to switch to being China's
I don't know. China is pretty successful so far in "solving Ukraine" by propping up the moth infested bear pelt USSR animatronic that is Russia.