Evidence of marriage

Yes, you do need to prove you are not legally separated.

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Will I be bar with d 10 yrs penalty? I am from Mexico I entered D USA Territory illegally lived in NYC from 94/2011. 18 yrs

Since you will be providing all truthful information, it will be evident that you lived in the U.S. without permission and are subject to the 10...

In the naturalization form(N-400), there is a question about entry and exit from usa. They're asking all the exact dates.

You have to do the best you can.

Registered to vote as LPR. Do I meet the standards for the 3 exception conditions during naturalization processes?

I don't believe so. You need to prove you believed you were a US citizen.

Can I apply for J1 scholar waiver if I've left US for 1 year?

Even if you could, what could possibly be the basis for the waiver? You must not have any urgent need to stay in the U.S. if you have been gone...

Can I apply for J1 physician visa if I have my J1 scholar visa waived once

You should be eligible for another J1.

Can the wife of an OPT Holder ( H1B applied and accepted in Cap gap this year ) apply for a B2 VISA to visit husband ?

You should not come to the U.S. with intend to change visa categories after you arrive. It seems you have been eligible for an F2 and will soon be...

This question is for an immigration lawyer. Can the parents of a 3 year old take her to Cuba, come back and leave her there?

I am not aware of any law that prevents parents from taking their children to Cuba.

My immigration asylum case

Yes, under the Child Status Protection Act she should be included.

It can take up to 30 days.