What roles does L-1A holder need to be eligible for EB-1 while filing for the green card?

The roles are defined by the company's needs, not the L-1A requirements. Consult with an attorney.

What I need to do now?

You should discuss this case with the school's DSO.

Will the enlistment in MAVNI program will affect my H1B visa interview adversely?

You may be required to fulfill a commitment under the MAVNI program that would preclude you from accepting the H-1B employment. Consider both...

Do we have to live together ? Can i travel with the new visa status.

"paper marriages" generally do not meet the requirements of the US Immigration & Nationality Act.

What are my next steps if they deny?

USCIS will always consolidate the files before making a final determination.

It could be if the program is associated with the University. Consult with an immigration attorney.

he could sign an affidavit of support for you, potentially, but cannnot file an immigrant petition for you to accord you any type of status.

I-94

"Duration of Status," which means that you are admitted until the date your program is complete, as usually indicated on your Form DS 2019.

No, you should not need to register a foreign divorce in the US in order to marry. Check with the country registrar's office in Nevada for...

Can I apply a Green Cards - Aliens of Extraordinary Ability Applicants ?

This category is reserved for those people who are among the "best in the world" in their particular field.