H-1B失去工作后用EAD找工作如何保持身份， 请教Pjiang等大侠

I am currently holding H-1B visa, and my employment was terminated yesterday. My green card petition is on NIW with I140 approved, and I485 is pending. My questions are:

1. If my new employer will sponser my H-1B visa, when is the latest time they need to submit the petition to USCIS?

2. If I don't have my H-1B transferred to a new employer within the grace period, what should I do to maintain my status.

3. My NIW petition was not sponsored by my employer, am wondering if I am OK to stay with unemployment and how long.（I am currently holding a valid EAD though I never used it in the past.)