My L1B Ext was denied recently, can i apply L1A?

There is no "cooling period," but that would not be the issue in your case anyway.

Filing H1B transfer without having a proof/copy of I-129(petition), however I have the "Receipt Number"

It appears that you are subject to the H-1B cap, so any petition would have to be filed for FY 2016.

Hi, I'm applying for I-485 marriage based, my usc husbands income is way below poverty guideline, however I have

Unfortunately, you will still need a joint sponsor. this can be any US Citizen or lawful permanent resident.

I need to know the immigration consequences after having a permanent injunction placed on a person in civil court.

Generally, only criminal convictions could seriously impact a person's immigration proceedings.

D.S-260 (Previous addresses since the age of 16), Impossible to mention Email & Telephone numbers on Form D.S-260.

He must provide as much information as he can, or indicate "unknown."

Extention of L2 with my I94 validity

She must be able to present ample proof that you are maintaining L-1 status to obtain the visa stamp extension.

This should not be a major problem, as long as the visa is still readable by the CBP.

EB2-NIW petition (change of field)

NIW cases are very complex and require a great deal of considered thought from the outset.

Will getting married to a citizen protect and immigrant who entered the U.S legally from being deported?

No, marriage alone offers no protection against deportation.

I just got married in New York, we are going to apply for the Green Card. While we are waiting to get it, can she work legally?

She should be issued a work authorization card in less than 90 days after filing the adjustment of status application and work permit application.