How to adjust from from pending asylum to family based immigration based benefit it also involves J1

Your scenario is complicated. If you have a strong asylum claim, i would wait for the decision. Otherwise, with your J-1 Visa and 2-year...

I have a question about u visa work permit

No. You cannot get a work permit until the U-visa is approved.

Can I re enter United States in B2 visa with in the 6 months I 94 time frame?

You already left the United States, so when you are allowed entry back into the USA they will give you a new i-94 at the port of entry.

I have my Case I 485 denied? there is anyway two requests for appeal ?

When they deny your I-485, they give you instruction on how you can appeal with the decision.

My asylum application with USCIS now 181 days elapsed ,fingerprint already done ,but interview IS not scheduled yet .

You could apply but does not mean it will get approved. There are some delays at the moment with USCIS for processing EAD. You need an attorney to...

I485 for mom, interview within 4 months?

There's no need to prove her non-immigrant intent when she came here on the visa. You are entitled by law as a US citizen to petition for your...

Based on what you stated, I see no problems. Just be prepared for questioning by Border patrol officers at the port of entry.

I went to my marriage interview was fast and they took my picture and fingerprint again ho do i know if it was approved?

They will send you a notice in the mail if the case has been approved, denied or if they want more information.

Does my landlord have the right to ban me from cooking in my studio apartment or can change the move out notice to 60 days?

It all depends on your lease. 30 day notice to move out is typical if you are in a month to month situation.

It most likely will not affect your mother in any negative way. If she has a pending Adjustment of Status Application, she will need to disclose it...