Can a green card holder sponsor a nephew for F-1 visa?

You need to communicate with the school that you have in mind as they will need to issue an I-20 so that your nephew can apply for the F-1 visa.

Can I re-apply for citizenship?

Your question is about reapplying for citizenship but, from your information, it doesn't seems that you ever had the time as an LPR to qualify....

My OPT was denied due to a mistake during application.

You can probably work this out with your university if your application would still be timely and they now have, or will, issue the recommendation..

I have been out of US for more than a year, is my greencard still valid?

You may have abandoned your residence but that determination can only be made by an immigration judge in Removal Proceedings. I you present...

Can i send the copy of documents to NVC?

Submit copies and bring originals to interview.

Yes, you can still use them if you have them.

I think my wife may have married me just to obtain a green card or immigration status change . who should I contact.

What you can do will depends on how far in the green card process you and your spouse are, for example, is she a conditional resident or has the...

Does a public intoxication ticket that occurred in canada count as a criminal record?

Ehe way you put it, probably not, but would have to look at the actual record to give you a definitive answer.

Can you get a student visa to come to the US to learn english?

Indeed you can get a student visa to come study English in the US. You need to find a school to issue you an I-20 so that you can get your F-1 visa.

Is my father eligible for a humanitarian visa?

If your father's I-485 is pending, he can get Advance Parole to visit his mother in Mexico.