Arranging visa for China. Will the 144 hour free transit apply in Shanghai and HK.

We arrive in Shanghai, staying four days before we embark on a cruise, first stop Tianjin Port (for two days in Beijing), South Korea, Taiwan and Japan. We disembark in Hong Kong where we have 3 days in Hong Kong before a flight to Xian for three nights. Flying from Xian to London via Hong Kong. Will our China entry permit be valid for our exit and re- entry to China? Also will the 144 hour free transit apply in Shanghai and HK.
Thanks
Katherine