As an-green card holder (Asylee), do I need I-131 to travel and come back to the US?

Just in case, I would get a travel document and not use your passport for travel. Although I have a number of clients who have used their...

Does my stay get affected?

Any absence, with rare exceptions, over 6 months breaks continuity of physical presence.

Can i travel I-551 stamp my I-751 waiver is pending.can I travel overseas

Yes, you can as unexpired I-551 stamp is proof of your permanent resident status.

What can i do to help her

you would have to rephrase your question to get a meaningful answer.

Dual citizenship is permitted in US but the US Government will still consider you a US citizen and you will have to pay taxes on your income...

Does the I-130 have to be approved by the time we go to court in April ? Or is a marriage certificate good enough ?

The case in the immigration court will have to be continued pending decision on the I-130 petition which to be filed right after you get married. ...

Waiver due to illegal entry

There are two ways - provisional waiver (form I-601A) which is to be filed after the I-130 petition is approved, and the cancellation of removal...

Can she continue staying beyond this date while waiting for GC to get processed or does she have to leave the country?

Your mother can stay. However, if she needs to leave while her I-485 is pending she can do so only with an advance parole document (Form I-131).

I-485 Interview Question

You never filed I-485 for your wife. It's an application and she filed it on her own behalf on the basis of the I-130 petition that you filed for...

You may not have been eligible to get a green card in the first place for 10 years after the grant of voluntary departure if you did NOT leave. But...