F2A concurrent filing possible?

Yes.

Will I be able apply for Travel document or Advance parole while asylum pending?

Depends on where you are planning to go.

Student visa

Talk to the DSO to see if you can go back to student status. It will depend on how long you overstayed.

Can I transfer my H1B if the current employer has started initiating H1B Amendment?

Yes you can file a H1 transfer while the amendment is pending. Get the new employer to premium process the case. Once it is approved, you can have...

How does the USCIS verify that the person who translated a document is certified to do so?

The translator certifies that what he is translating is true. Nothing further is required.

How will Immigration Officer look on my sponsor? What are they looking for?

As long as your uncle meets the financial requirements, you should be fine.

What is the maximum stay with a visitors visa?

Check to see when your I-94 expires. As long as you leave before then, you should be fine.

Do I have to leave the country if my R1 Visa (I-94) has expired and my Work Authorization (I-129) is being processed?

Yes, you can stay. You will be issued a new I-94 with the extension approval.

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Will my fiance be eligible for a green card once we get married? Even though she is on deferred action? how long will it take?

If you are a citizen, she should be able to get a green card. I suggest talking with an attorney to get the details and timelines.

Pending I-130 petition for spouse of an LPR

Contact the NVC