72 hours transit in beijing

Hi
I am flying from Tokyo (hnd) directly to beijing (pek) . I have a united kingdom passport. I am having 64 hours in total in beijing, and then flying out from beijing (pek) to Krabi (kbv) in thailand. I have the flight ticket to show for my outward journey. 4 questions if you you don't mind
1) am i eligible for the 72 hour visa-free transit?
2) can I get the free transit at the airport in beijing (pek)?
3) do I have to go to the police station to book in?
4) can we leave the city of beijing for a few hours to see the great wall of china?

I am fairly confident I am ok but still a bit nervous and don't want to make a mistake!

Thanks Mike