We had the opportunity to visit a laundry while on the trip. When we arrived at Shanghai we simply let the hotel take care of the laundry. It really was not that expensive. As for shoes, go for comfort. Tiananmen and the Forbidden City will take you about four hours so think comfort.
I'm thinking you can buy an extra bag in Hong Kong because the limits on the international flights will be much higher - 2 bags/person @50 lbs. each.