Both Petition and CoS approved,but do I need a stamping to start work?

I was in US on H4 visa. My H1B petition was filed in the month of June 2012 with automatic change of status. Later an RFE got raised and it continued in that state until Nov 2012. Meanwhile I traveled outside US to my home country India in the month of Nov 2012 and got a stamped H4 on 28th Dec 2012 and returned to US on 29th Dec 2012 with a new I94.
On the same day i.e 28th Dec 2012(the day I got my H4 stamped) my H1B petition was approved (for a period of 2 and half years),with a approved change of status.

Below are few questions that I have regarding my current scenario:-

  1. Although my CoS got approved,my lawyer says it was done by mistake and right now I am on H4 and I need to go for a stamping to get my change of status done, Is going to India or some other country and stamping the only option? And are there chances of rejection or any complexity?

  2. While I being in US, can my employer file for only a change of status (I 539) ? If yes, roughly how long will it take ? And is a premium processing available for only COS? (so that I don’t have to travel outside US)

  3. Is there a possibility that my H1B gets invalid, if I don’t start working for a certain number of months / or don’t get my change of status done within x number of months.

Your lawyer is correct that your COS was approved in mistake. Your options include either going to India for stamping or filing I-539 while continuing to be inside US. Its preferable not to go to CA or MX as you didn’t do Masters in US and this is your first stamping. Chances of successful stamping varies from case to case.

H-1 will not become invalid if you don’t file for COS or enter US on stamped H-1 visa. You can do this anytime during the petition’s validity period.