visit China family

My mother and I are on our way to China to visit my former exchange student and her parents. They have invited us to stay in their home and will be taking us to see a portion of the Great Wall and the Terra Cotta Warriors. Is there anything we should do about an extended stay, for example should we leave money for the extra cost of housing and feeding us? Additionally I LIKE house work and keeping things tidy but don't want to offend our host and hostess. Can I offer to wash dishes, etc... without causing offence?