請教父母移民的問題

My parents in states with me right now. I plan to apply green card for them . I have two questions. Please give me some help. Thanks!
1. During their waiting period ( waiting for green card), do they have to stay in the states? If they need be back to china for a short period, what should they do?
2. My parents Hu(4) Kou(3) in Nanjing, and my sister lives in Tianjing. Can my sister help my parents to get their 'parents certification" and my "birth certification" in Tianjing?

Thanks for your replying.