72 hour visa uncertainty

I am traveling from the US to Beijing, and will be staying there for under 72 hours.
Then I am flying to Thailand for 2 weeks.
After Thailand, I will be flying back to the US, and not connecting through China.
My questions are:
1. Do I qualify for the 72 hour free transit?
2. Can I visit the Great Wall from Beijing without violating that 72 hour free transit?
3. What papers do I need?
Thank you.