72 hour visa free qualified?

Please tell me if my following trips is qualified for the 72 hour free transit?

TPE-PEK on airline A, PEK-MFM-TPE, on airline B, two one way tickets.

1) Does the entire itinerary have to be on the same single ticket? Or can I just show them my onward ticket on airline B at immigrations in Beijing?

2) Even though my final destination (TPE) on my return trip is the same as my originating country, I am making a connection in Macau for my return trip, will that qualify as my return destination instead of Taipei? Or should I play on the safe side and do a stop over in Macau instead of just a connection?

3) Finally, does Taiwan, Macau, and Hong Kong all qualify as their own region/country to do this? Or does the Chinese government view all three (technically only two) as one?

Thank you very much for any assistance!