transit visa and application

I am trying to travel to Nepal from USA, I have a layover in Kunming with a stopover in Tao. I will be in and out of entire China in 24hr. With the 24hr twov am I allowed to leave the airport? Also, am I able to get more than a 24hr twov in case of flight delays? I have a USA passport. Are these visas something I have to apply for and have before traveling, or is it something I receive at the airport in China?