Extremely doubtful you are allowed to leave the U.S. while you are on probation.

What is the contact information for the New York DHS district director?

Actually you need ICE, which handles arriving alien issues. Generally they will not release arriving aliens who may be subject to removal. ...

Should I let immigration know about martial status?

On your citizenship application, you will include all of the relevant information. That is what they need to know.

RFE on Spouse's EAD

The I-140 approval notice will be sufficient.

If i can process 2 immigration case

Your sister can file for you, and if you get married, your spouse can also file for you.

Can I transit in the USA from France to fly to Brazil if I am currently applying for a green card? Can it hurt my application?

Not enough information. Is the visa available now? Are you seeking admission into the U.S.?

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Can a spouse succesfully complete I-130/etc US petitition his/her parent if he/she did not work at all in the US?

Yes, you can do it, you just need to prove US residency and provide a joint sponsor on the 864.

Can i join college with Pending COS to F1 . My H1 is expiring.

I believe that the Designated School Official will tell you no, you cannot.

How can I learn if someone has been deported or is in the process of it being done?

1-800-898-7180. Enter the Alien number and it will provide information if the person is now, or has ever been in removal proceedings. It will not...

I had a H1B petition approved in the year 2000. I worked till 2001 in the USA and returned to Bangalore, India. Cap-Exemption?

You are subject to the cap. People are exempt only if they are currently in H1b status.