Flying from Seoul -> Beijing -> Tokyo

John, your itinerary, under the assumption that you do not have any other landing within it, is definitely and undeniably eligible for 144 hour visa free transit in wider Beijing area. It is 144 and not 72 hour visa free transit in Beijing.

You are allowed to travel on separate tickets and on unrelated airlines as long as your itinerary is eligible based on Country A - Country B (China) - Country C concept. Your itinerary is eligible and upon landing in Beijing you will present your tickets at 24/144 hour visa free transit counter in order to be granted to exit the airport.

You can stay at your friend, but you should have in mind that you will have to register, within 24 hours upon your landing, at the closest PSB. Your friend can assist you. Also, have in hand the full name of your friend and her/his address where you will stay along with her/his phone number because you will be almost certainly asked about these details. Have a nice journey.

Hi there: I am a Canadian passport holder travelling from SIN to PVG - my stay in PVG is 2 days and then my outbound from PVG is to HKG. Does HKG qualify for purposes of this visa-free transit?

Yes, HKG is qualified for the visa free transit.

Dave, the answer is - yes. Hong Kong is an eligible territory as far as 144 hour visa free transit is concerned. So, if your itinerary is exactly:

Singapore - Shanghai - Hong Kong

And you do not have any additional landing between those points, you are definitely and undeniably eligible for 144 hour visa free transit in wider Shanghai area.