Can I apply for I-485 after one year of my asylum approval while I got I-485 denial one time before because of my EB2-NIW?

Even if you are out of status you may file for adjustment based on an approved asylum application.

Will we face any adversaries getting a green card/work visa if we get married given my background? Are there any other options?

Unless the convictions relate to violations covered under the Adam Walsh Act they should not impact eligibility.

EAD expedite - what's the meaning of this correspondence

You may want to ask the Senator's office for clarification but a job offer is not a basis to expedite processing.

Travel outside the country while I-140 application is pending

No travel outside the US do not affect the I-140

Should I fight a losing case? Any concessions state might make to help me from the immi standpoint? Like a record entry etc?

it may be a CIMT and a withholding of adjudication may be considered a conviction. Take your charging documents and any other related information...

On RFE letter, it said my joint sponsor's income didn't meet 125%. can i send doc of a new joint sponsor?

Yes but new cosponsor must meet the income requirements.

Filing form n-400

If your spouse has never married previously enter zero.

If I get asylum granted in interview, can I apply for I-485 one year after asylum granted while I am out of status?

Yes you may file for adjustment if you are out of status and the asylum is approved. However, if the asylum is not approved you may then be out of...

Provide a copy of the resident card. Make sure to follow the instructions for the form fully.

Is it possible to get greencard/citizenship based on the reason I've explained below

It is possible if you have an employer willing to petition for you using a labor certification process. it is not possible using a self petition as...