1) Airport lounge access 2) Transit Visa at Beijing Capital Airport

I will be arriving PEK Terminal 3 at 5:00 AM and have connecting flight after 14 hours at 7:00 PM.
As Star alliance Platinum member, I have access to lounge.
Questions -
1) Can you take a shower and sleep at lounge?
2) As US citizen, can I get transit visa to visit the city for few hours?
3) How far is airport from some key tourist places?

Andy Desai