Other than the aborted Yuan expeditions, were there any times in history where China attempted to exercise direct rule over Japan, whether through conquest or some sort of dynastic arrangement (i.e. more than just a tributary relationship or purely nominal suzerainty)? If not, what would have been the best time for a Chinese dynasty to make such an attempt, and how successful would it have been? Could China have ever conquered and held all of Japan? And if so, how long could Chinese rule in Japan have been maintained? Is there a scenario where Japan could remain in China for so long that it comes to be seen as a region as integral to China as OTL Manchuria? And, would a Chinese Korea be a precondition or necessary corollary of a Chinese Japan?
Lot of questions, I know - feel free to answer whichever you want.