Two layovers in China on the way to Nepal - does the 72 hrs free transit apply?

Hello,
I've read the answered questions concerning the 72 hour Free transit, but I am still not 100% clear whether this applies to my situation.

I am flying to Kathmandu, Nepal in November. I have a 2 hour 20 minute layover in Bejing. From there I fly into Chengdu, where I have a 12 hour layover. Flight time from Bejing to Chengdu is approx. 3 hours.

I am coming from Washington DC, USA, but I am a German passport holder.

I am planning on leaving the airport in Chengdu, to spend the night in a nearby hotel. Does the 72 hour free transit apply here? Does the time start in Bejing or in Chengdu? Do I have to mention it to the airline in Bejing or wait until I land in Chengdu?

Also, I am planning on getting a tourist Visa for Nepal at the airport in Kathmandu. Will this matter?

Thank you very much for all your help. This is my first trip to Asia.