144 hrs free visa

I'm planning to spent my summer holyday in Asia. My flight shedule is :BUdapest-Beijing-Shanghai (by bullet train)-Manila-Hong Kong-BUdapesta. I'm plannig to stay 2 days in Beijing, 2 days in Shanghai and when we depart 2 days in Hong Kong and Macao.

I live in Romania. Do I qualify for 144Hour Free Tranzit? If yes, can I land in Beijing and depart to Manila from Shanghai?

Thank you,Liana