When my I-751 application is still pending status, can i apply for N-400?

A person with a pending I-751 qualifying for naturalization may file an N-400.

USCIS identifies the sponsoring employer by the Federal EIN. There are strategies that can fix and / or benefit from this confusion.

A valid foreign passport is not required to naturalize..

My sister in law had her citizenship interview all went well.

There are on occasion delays with review following naturalization interviews. Nothing to do but wait..

Will a warrant of arrest Show up in H 1B Extension filing.

The arrest warrant will show. It will not be an issue for the H extension. It can be an issue for a visa renewal.

Can an exempt employee work part-time on the side? If the employee is on h1 visa and a concurrent h1 be obtained.

Concurrent H1B employment is available to a person employed in H status and the current employer is not required to be notified.

Is it ok if I don't keep a physical address in the US while I'm out of the country for a long time?

While it is not required to maintain a physical address in the US. Intent to reside in the US is required with reentry permits.

Is my marriage legal?

Generally, a marriage meeting the legal formalities of the country in which the marriage took place is legal for US immigration .

Am I a US citizen ( green card holder since 12 yrs old) if my mother is a US citizen?

a green card holding child is automatically a US citizen if the parent became a citizen before the child turned 18 and if the parent was a citizen...

Is it possible to use work visa to work for someone and be self employed too?

Generally, employment visas require all work to be for the sponsoring employer or employers.