Visa to enter China for holder of Singapore ordinary passport.

I am holder of Singapore ordinary passport. I intend to travel from Singapore to HK to Hangzhou and Taipei and back to Singapore. Each location is 4 to 6 days. Do I need entry permit when entering Hangzhou?

I under Singapore ordinary passport holder need not require visa if the stay in China in less than 15 days. How about the 72 hours transit exemption? I noted Singapore is part of this programme. I am confused. Please advise.