passport name change/ spouse & child's visa

I am a Chinese citizen with a Chinese passport and a US green card. I plan to travel to China with my American husband and our toddler. I have some questions:

1. I changed my name after I got married. My Chinese passport does not match my green card or my driver’s license (both have my new married name).
a. What forms and proof documents do I need to update my Chinese passport?
b. What is processing fee?
c. Do I have to go to the consulate in NYC in person?
d. How long is the processing time?
e. Can I get it expedited so I can get it processed on the same day? I do not live in NYC.
f. Can they mail the updated passport back to me or do I have to get it in person?

2. My husband and child are both US citizens. We are visiting my Chinese parents.
a. Do they both need visitor’s visa?
b. Does my toddler need her own US passport for the Chinese permit?
c. Do they need to apply in person?
d. Where can I find an authorized application agent?