I am US citizen and traveling with family (all US citizen)

I bought ticket los angles to kathmandu (transit in chengdu for 19 hours), I can get free visa right?
My return ticket is kathmandu to Kunming (16 hours transit), KM to Nanjing 23 hours transit, then nanjing to los angles.
I think I am eligible for free transit visa for Nanjing, right?
What are the option for KM? Does it have hotel inside the airport so I can stay there?

thank you very much
Chandra Lamichhane