Single versus Double Entry- 72 hour Transit Visa applicable?

I am going on a student trip to Beijing, have a round trip ticket to PEK, the program ends in Shanghaii, and I will be flying to Hong Kong from PVG, staying for 3-4 days, then flying to Osaka, Japan, from HKG to visit my brother and his wife for 5 days, and flying from Osaka back to PEK on the 15th, to catch the original round trip flight back to the US (DCA). I read of the transit policy, and was just curious if this would apply to me, as all of the flights (PVG to HKG, HKG to Osaka, and Osaka to PEK) are one-way tickets. The only round ticket trip is from the U.S. to PEK- the one that I would be catching when i fly back from Osaka, and I may have to fly in one day prior, and need to stay in Beijing for one night until my flight leaves at 6:05 PM.
Will I qualify for this? I am obviously already needing a single entry, but do I need a double entry one? or will a transit permit be acceptable for that last re-entry? (Also I saw for tourism, Hong Kong allows stays for 90 days for US citizens- so do I need to do anything for the flight from PVG to HKG?)
Thank you!