You do not need advance parole (and are not eligible for it). You can travel and re-enter the U.S. with your expired green card and the I-797...

If you are out of the U.S. you are not in H-1B status (you only hold nonimmigrant status when you are in the U.S.) - you can stay out forever. ...

Do I qualify for premium processing in my case ?

Have you asked your employer's immigration counsel ? The petition you describe is not an H-1B extension, and thus can be filed via premium...

If I marry my immigrant boyfriend, can he become a permanent resident and is my boyfriend here legally?

No, his passport alone does not allow him to remain in the U.S. legally. If you boyfriend entered the U.S. lawfully, and you marry him, you and he...

Approved I-140, eligible for EAD?

The new rules only allow an H-4 to get an EAD if the primary H-1B has an approved I-140. If you have an approved I-140, your employer may be able...

I was in US on F1 visa from 2004. My OPT end date June 2012. I returned home Feb 2013. F1 Visa expiration Dec 2014.

Yes you overstayed and violated the terms of your F-1 status by remaining in the U.S. more than 60 days after your OPT ended.

Will getting a divorce after 2 yrs of marriage affect my green card?

Since you likely have conditional permanent residence now, you will need to apply to remove the conditions 90 days prior to the expiration of your...

Citizenship requirements

The continuous residence requirements start from the date you became a permanent resident (even if conditional).

Travel to mexico , need VISA if on H1B in USA ?

It depends on what country you are from. You need to check with the Mexican Consulate.

I140 transfer along with H1 transfer

Unless you are in the I-485 stage for at least 180 days, if you change employers, your new employer will need to restart the permanent residence...