Change of Status from H4 to approved H1B

I am currently on H4 visa (Valid till 2018) Living in US. I had applied for H1b from a consulting service and got approval also.But I travelled to India on an emergency during that period. I am back and currently in US.

Today I received the notice stating that my H1b is approved and as i travelled out of country my current status is still H4 , since I went out of the country and also stated that I have to go to consulate in India to get my H1 stamped.
My Questions :

  1. Is there any way to reapply for change of status without travelling to India ?

  2. How long i can stay on H4 without changing status even after H1B approval.
    3.Can i start searching the job in USA on H4(which is my current status) with my employer, and after getting job should go for stamping in india and start working in USA.

  3. If I go to India for stamping what are the chances of getting it stamped ?

  4. How much would it cost to reapply.
    6.Without offer letter, are there any chances to get the status approved.

Please Advise.

Thanks for the help

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