Tokyo - Beijing - Tokyo

Hi,
I am planning to visit a Beijing friend. The plan is to go from Tokyo to Beijing and then back to Tokyo. I would be staying at her house during my trip.
-Can I apply for the 72h visa exemption?
-Do I have to mention the exemption to the airline that I intend to use the 72h entry permit exemption when purchasing the ticket or when I check in?
-When do the 72 hours start counting if I land in Beijing? I read that it starts as soon as you arrive, meaning that if I land on february 19 at 8 pm, you can't stay longer than february 22 at 8 pm, is that correct? Can you please write me an example of dates and times so I can see it more clear?

Sorry to ask these many questions, I just want to do things right and not get into trouble.
Thanks for your time.