Question about visa of China - travelling between two/three countries of China/ transit

I booked a round trip tickets as following:
19-05 Ams-> PVG (20-05)
22-05 PVG -> TPE
27-05 TPE -> SIN
30-05 SIN -> CXR (Nha Trang/Vietnam)
09-06 CXR via CAN-> AMS (10-06)
My question is do we need a visa for travelling from Shanghai to Taiwan, cause Taiwan is a country in China and we staying there for couple of days. For Shanghai we can using the 144-hour transit for free. At the end we making a transit via Guangzhou, it is only a transit do we still need a visa because we travelling at the beginning to Taiwan ( China part) and last via Guangzhou ( China part again)?