What all needs to be done for spouse name change

[Kart2004]

Hi,

My spouse in in India, I am in the US.

We got married in Jan 2007. Our marriage certificate has my wife's name before the marriage. I also got her H4 done (which also has her old name, the one before marriage).

Now she applied for a name change and got the govt. document. Since her air ticket to India is issues in the new name, I think she will have to apply for her new passport (reflecting her new name).

My questions are:

1. Is all the above right?
2. How much time does it take to get the new passport (Pune)
3. The marriage certificate has her old name, so is it a problem?
4. When the new passport is issued, do they change the name on the VISA automatically? Or does it need a trip to the VISA office?

Thanks for you help.