China, Beijing 72hrs free transit visa.

I am a German passport holder, and i will make a stop over of less than 30hour at beijing airport. my route 28sep FRA- 29sep PEK by LH & 30 sep PEK-SIN by SQ. i am flying from frankfurt and my final destination is Singapore, so i have 2 different filght tickets by two different airlines. The first flight ticket allows to reach beijing airport, i will have to get my baggage, and i plan to go for a walk in the city then come back to the airport the next day and register to be able to take my second flight.
All within 30hour, am i able to apply the 72hrs free transit? or i will need to apply for one before i enter beijing ?

what if i am holding on to 1 ticket same itinerary FRA-PEK-SIN but two different airline this is okay for the 72hrs free transit right?

many thanks for you help.