H1B transfer before visa has been stamped on passport

I work for employer X in USA who filed for my H1B this year and it has got approved last month. I have the documents of my approval but have not yet gone to India to get my visa stamped on my passport. Due to some reasons, I am thinking of switching my job, and I have got an offer from employer Y, which does both transfers/new filings on H1B.

  1. If I decide to switch to company Y, will my current employer (Company X) be able to revoke my H1B visa status?

  2. Is there any probability under which I can become out of status?

  3. What are some of the important information I should know and the documents I should have from my current employer to ensure I do not fall in any immigration related issue?

Please note - I was under F1 status prior to my H1 getting approved (with OPT, which was valid for up to 3 years).