EAD Question for Employment based I-485 Process

Well, I would answer YES, and add a copy of your OPT. Ask her to attach copies of the OPT cards.

Travelling with H1b extension pending

It all depends. Premium processing means that in 2 weeks USCIS has to make a decision, but often they issue an RFE and then the process takes much...

SSN Problem - Applied for SSN around 3 months back, Still waiting to get it.

What is your status? Did you bring the proof to the SSN administration?

Can someone on a nonimmigrant visa marry a GC holder while in the states and leave the country during the process?

Can travel : yes, but with an advance parole. Otherwise, the process will have to be restarted.

Petitioning H1B

You have to be employing this individual. Consult with an attorney. The process is not as easy as you may think.

Naturalization interview result

An "Armenian:" usually means nationality. Your wife needs to see an attorney.

Consult with an attorney who was handling your application for company B.

Will I face any problems to re-enter the US with an advanced parole?

You should not. Just don't go to your home country and prepare to answer questions regarding your travel when you will be coming back.

I will file an I-130 (petition for alien relative)

There is no such a thing as an "illegitimate child" anymore. She is your daughter. I do not have a middle name, for example. It is not a problem ...

F2 dependent, can i convert back into B1/B2 visa for medical residency to be eligible for H1B visa?

Is your F2 expiring before the H1B may start? Consult with an attorney.