Once you are separated with your current employer, your H1B status is no longer valid. And there is NO grace period theoretically. If nobody is serious, you are OK. But if somebody picks it up in the future and fond you have a status gap, you'll be in trouble.
You have secured your H1B quota from your current job. You don't need to worry about the quota next time if you got a new job.
You have secured your H1B quota from your current job. You don't need to worry about the quota next time if you got a new job.