can i apply for transit visa at the beijing airport?

hi i am in australia going to transfer airline in Hong Kong and then i am travelling to beijing aiport to go to mongolia.

First entry is less than 12hour stay in beijing so i am eligible for free transit. but second entry is from mongolia to beijing and i arrive at 21st may 2pm in bejing. my next flight will be 24th 6:30pm.

would i be able to apply for the free transit for both of entries? and can i apply for transit visa at the beijing airport? or should i apply for it here in australia?