H4 to H1B information request

[ds160h1b]

Hello all,

I was working on H1B visa which was valid until 2018. I recently got laid off and hence I applied for COS to H4 a few days after, through my spouse's company. The application has been submitted but still waiting to receive receipt# etc., I may receive an offer letter from a company in a few days which is willing to file my H1B. I've a few questions that I'd like to get some clarification.

1.) Is it possible for the prospective employer to file for a H1B, while my H4 is still under process (H4 is not approved yet) ?

2.) Does the new employer has to file a COS from H4 to H1 along with the new H1B application?

3.) Given these circumstances, when can I start working for the new employer?

4.) I'm also hearing that I need to leave the US and travel to my home country and re-enter to validate the new H1B visa. Is this an option to be considered ONLY if the new employer is unwilling to do a COS from H4 to H1?

Thanks in advance.

[ds160h1b]

Please reply as I'm need of some guidance here..