If I visit the Great Wall closest to Beijin, is that considered leaving the transit city?

I am traveling from US to Singapor round trip. Two questions:

1. I have a 10 hr layover time in Beijin on my outbound flight from US to Singapour and a 23 hr layover time in Beijin on my return flight back from Singapor to the US. Outbound and Return flights are one week apart. Can I get a 72-Hour-Visa for both: my outbound and return flight?

2. Is going to a section of the Great Wall near Beijin considered leaving the transit city?