Green card unemployment benefit

Yes, why not? You are eligible to work...

Can I get a labor certification visa if I was illegal in US?

You cannot get an employment based green card if you are out of status and do not qualify for exceptions.

Maybe. You need to consult with an attorney, especially if you filing for adjustment of status.

H1 To H4 Transfer with Valid H4 Petition

I might be confused, but if your husband has H1 now, you should apply for change of status now.

Check with them. I would think it depends...

US passport with Mother's certificate / other early documents

Well, the problem is for international travel, you also might have to have a passport for the baby. So, you might want to reschedule the trip...

Follow to join benefits?

Provided, he was in the application, I-824. Read instructions to the forms at www.uscis.gov

F2 change of status pending travel abroad.

You should send a copy of your visa with an explanation of what happened.

What evidence is best to resend I-751 , after receiving that the evidence submitted with our form is insufficient?

You have to consult with an immigration attorney ASAP. If I 751 is denied, they issue Notice to Appear.So, you have to present requested evidence...

Hi

Your work permit should be issued within 90 days of your application. However, sometimes there are delays.