Is stamping required after transfer?

[Rahulg]

Hello,

I worked with "Company 1" on a H-1B visa for "Client 1". My Visa with "Company 1" is valid till April 2016.
After an Year, I have accepted a job with "Client 1". I have an approved petition (I-797) with "Client 1" , valid for another 2 years

I am planning to go to India in a week's time and return to US after 1 month.

Please advise on the following.

1) Should I go for visa stamping now? Because I am no longer working for "Company 1" through which I got the visa stamped (even though the visa is valid till 4/2016)?
2) What are the scenarios in which we need to go for visa stamping (even when you still have a valid visa)? Would it be an issue, when filing for GC, if we don't have the visa stamped (even though we have an approved 797)?
3) When travelling back to US, is it sufficient if I carry only the approved petition with my new employer? Should I be carrying any other documents in addition to the approved 797 forms

Thanks