Two visa questions

Hello! 
My family (4 in total - 2 adults, 2 children) are all US citizens who are considering visiting China in July. My questions are:

#1. Do children pay the same price for visa ($140) as adults?

#2. My passport will expire in December (about 5 months from when I plan to visit). We only plan to stay for a week, but I know some countries require 6 month passport validity. Will this be okay in China?

Thank you for your time,

David