I am arriving at Pudong airport Shanghai and departing from Hongqiao airport.Do i need transit visa?

Hello,
I am coming from Taiwan and going to my country-India. I will arrive at Pudong and depart through Hongqiao,layover around 20 hours.We dont come in for 72 hrs transit facility,like some other countries.
I want to know-
1,is some transit type required for transfer between Pudong and Hongqiao?
2,can we go outside the airport and take some hotel for overnight stay,if we dont have transit type?