Visit Shanghai via Taiwan

Dear Sir/Madam, My daughter and I are planning to visit friends in Shanghai in mid July via Taiwan. I have both Taiwanese and Belgium passport and my daughter has only Belgium passport. Question 1: our tickets to Shanghai will be purchased in Taiwan, do I have to proof the booking to apply Chinese visa here? Question 2: if I hold the Taiwanese pass (???) to enter China and my 9-year-old daughter with Chinese visa, is it a problem? I would appreciate very much your prompt reply, thank you very much.