Is it possible to travel from Shanghai to Taipei and then to Macau? What documents are used to book a ticket?

As long as the documents and endorsements are complete. Now many international airline official websites do not require documents to book tickets.

To go to Taipei, you need a mainland resident to travel to and from Taiwan, and to go to Macau, you must use a Hong Kong and Macau passport. It is recommended to use an ID card when booking air tickets, so that it is convenient to issue tickets at the airport

If you are a group, they will definitely help you solve it, but if you are an independent traveler, then when you buy a ticket, it will have a reminder