Self Sponsor H1B or H1B to F1/F2

Hello, I am currently on F1 visa(stem extension) and my H1B picked in the lottery this year. Due to the current market situation due to COVID19 I am a little worried. I have the following questions:

  1. Is it possible to COS from H1B to F1 (if intend to pursue a second master/Ph.D.) or H1B to F2?
  2. If H1B to F2 possible, Can I apply for a job on F2 and come again on H1B provided that if the employer is willing to sponsor?
  3. What is the grace period for H1B during COVID19, if laid off on H1B.
  4. Is it possible to start a business on H1B(during 60 day grace period)/F2/H4, and incorporate my own business and petition for self to obtain H1B?

Thank you

You cannot self petition yourself for H1B.

You can file change of status applications.

Thank you @Anil_Gupta