SIN-PVG, SHA-TPE-SIN, free visa for arriving and departing different Shanghai airport?

Hi,

I'm planning to fly from Singapore to Shanghai (Pudong PVG), site seeing for 2 days, then leave from Shanghai (HongQiao SHA) to Taipei (TSA). I have a US passport. 1. Am I eligible for 72hour free? 2. Does it work if I arrive and depart from different Shanghai airports?