24 - 72 - 144 visa exemption

I am purchasing two tickets. Vancouver to Bejing return and separate ticket Bejing to Mongolia return. I am planning on spending more than 72 hours in Bejing before proceeding to Mongolia. Will I be able to obtain a 144 hr free transit or do I have to keep it within the 72 hours. I am going on a Bejing tour so will be staying in the Bejing area.
I am returning from Mongolia to Bejing then to Vancouver two and half weeks later and will be transiting between flights and will require a 24 hr free transit. My question is how long between connecting flights should you leave if with the same airlines. There is connecting flight with Air China that is only 1.5 hours. Otherwise seems like a long time to sit in the airport.