Not at this time as this would constitute employment.

I am offered a fellowship from an NGO, and I am on H4 visa. Can I accept the stipend for the same?

Any remuneration for services rendered would be deemed employment and a violation of your H-4 status.

Can a us citizen brother can sponsor me and file an immigration petition on my behalf ?

Yes, your brother may do so but it will be more than 12 years before you may return to the U.S. as you may not remain here while the immigrant visa...

Earned a masters degree and continuing as PhD student. Am I eligible for green card?

To be eligible for a green card under the scenario you describe, you would first have to be secure employment through a company that would sponsor...

Can a non Mexican citizen apply for asylum at US port of entry in Mexico?

To file for asylum, one must be in the U.S. If one were to be captured crossing the border, the CBP officer would conduct a credible fear...

Change of status from H-1B to F1 student within the U.S.

This question has been previously answered. Please see prior answer.

I797 original is mandatory for filing cap exempt?

You did not disclose sufficient information to address your question.

Asylum application adjustment

Did you get denied for asylum by USCIS or Immigration Court? If the former, you will be referred to Immigration Court if not in status and may...

The N 400 application it asks if you were ever in jail or prison , seems simple enough ... However does that include ICE?

Yes, an ICE detention is an arrest for this question. As to removal proceedings, were you required to appear before an immigration judge or court?...

Can I live abroad while waiting N-400

No, you are supposed to wait in the U.S. during the entire process unless there is an emergency justifying an advance parole. Your description...