1. Your status does not automatically revert back to H-4. You would need to either file a change of status before terminating your employment or depart the United Stares and re-enter with a valid H-4 visa.
2. There is no grace period if your employment is terminated. Your status automatically terminated upon termination of employment.
3. You would need a new H-1B petition. You would be cap exempt assuming your prior employer was cap exempt.
Answered on Jan 12th, 2016 at 3:59 PM