Can i travel to Mexico and stay one week there and came back to USA with my green card that just receive 2 moths ago?

Yes you can as long as your Mexican passport is valid.

HHi my parent file I-130 under marred son category F3?

You must wait under the FB-3 quota which will take at least 6-8 years depending on your country of nativity

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Travel based on previous employer’s stamped visa while working for current employer on h1b receipt?

Yes you can. Your also need a current pay stub. Why don’t you ask your attorney?

It is clearly not a renewal of OPT. GOOD LUCK.

I just submitted my n-400 application for citizenship, can I cross to Mexico in a monthly basis for less than 24 hrs each time?

That will be fine. “Reside” is not the same as physical presence

Regd. H1 B transfer from Company A to B

You should wait for the decision on the RFE. If it involves the specialty occupation issue and it is handled properly it should be approved.

H1 extension beyond 6 years while Transfer is in pending status

Yes it is possible but you have at least one if not two Immigration attorneys you should speak with.

HOW IS THE QUICKEST WAY TO GET MY HUSBAND OF 17 yrs PERMISSION TO U.S.?

You should consult with a Board Certified Immigration attorney. Good luck.

My h1b got rejected because of specialty occupation and I am on valid opt stem ead until 2021. Can I travel to India now?

You should never travel on OPT and should never lose an H-1 on the specialty occupation issue. That is just bad lawyering.

I-140 filed with request for duplicate PERM from DOL still not approved

Doesn’t your attorney know what to do in these situations.