Does a denial of a bona fide asylum application prevent one from being eligible for a green card in the future?

No, being denied one benefit does not make you ineligible to receive another benefit for which you may qualify.

It is likely possible that you can pursue this path. However, more information is necessary in order to be able to say for sure. I suggest you...

Can she submit i-131 forum for me if am out side USA

More information is needed to properly address your inquiry: what is your immigration status?

Can I avoid deportation

More information is needed in order to give you an appropriate response especially the legal status of your mother in the U.S.

If I self-petition under WAVA, can my LPR spouse be denied citizenship due to cross reference and questioning of good character?

Based on the facts you stated, it does not appear that your husband will be negatively affected since there have been no arrests made or anything...

If an application to adjust status is denied, do I get to keep my priority date for future applications?

The priority date follows the date the application is filed, i.e. it changes with every application that is filed.

I-485 approved but no answer on I-130 - Filed AOS concurrently

Congratulations. You should eventually receive your approval for both forms.

Am I eligible to apply for naturalization?

Based on the facts you presented, it appears that if you are not eligible to apply now, you will become eligible this year. I suggest you contact...

Can I be deported since I'm not living under their care? If so, how can I defend? Will I be able to file an I-751 separately?

You conditions will be removed based on the validity of your father's marriage, not where you live.

Who should sign G-325A forms?

Everyone must sign their own form. I suggest you have an attorney review the package before filing to avoid mistakes which can lead to delays and...