Do separate tickets allow for double entry?

I'm a UK passport holder and tourist. If I book an open-jaw (i.e. single PNR booking) London-Beijing / Shanghai-London - and then buy a separate open-jaw Beijing - Seoul - Shanghai ticket on a completely different airline, thus across 2 separate PNRs I'm flying: London-Beijing-Seoul-Shanghai-London over a 10 day period, can I get 2 separate, 144 hour visa-free entries - 1) on arrival in Beijing, and 2) on arrival in Shangai. Or, must my onward international transfer be part of the same booking I arrive in Beijing on? Also when you say I need to present an onward travel ticket - do I need to be actually checked-in for my onward flight - i.e. I have a boarding pass - or is a reservation sufficient - I ask because some airlines will not let me check-in until 24 hours before my departure from China, so I wouldn't have an actual boarding pass when entering China, but could have a print-out of an airline booking.