Is it possible to take a boat from Xiamen to Kinmen, then take a plane from Kinmen to Taipei, and then return to Shanghai from Taipei?

It's doable. By the way, take a look at Kinmen, although it is a small village, there is nothing to see

Flying from Kinmen to Taipei is a small plane, and the luggage limit is 10 kg per person. This has to be considered. It is for reference only. I originally wanted to take this route. I checked it on Ctrip and gave up.

Generally, you take the small three links, that is, you go back and forth through the Golden Gate. You should be fine walking this way. Buy tickets in Xiamen in advance, the mini three links are still very convenient and cheap.

This is no problem. There are many flights from Taipei to Shanghai.