"Have you ever been refused a US Visa, been refused admission to the US, or withdrawn your application at the port of entry?"

Yes you were refused a student visa.

My spouse already lives in the US, how do I answer the question on DS-260 "Is your spouse migrating to the US with you?"

If your spouse is not applying with you then the answer is no.

Do i have to pay fee for i 765 when i already applied for i130 and i485 ?

Inter file the I765 with pending case.

Those two things should not be incompatible, however, USCIS might question some of your statements in the asylum case to make sure they were not...

Not applying for permenant green card?

She has to file to lift the conditionality or she will fall out of status. You have a lot of questions and you need a consultation.

How could I find out if there is a VAWA petition granted against me?

Write to USCIS and tell them if you suspect fraud.

How to correct a mistake in I-539 which is filed with H1-B Premium Processing

You don’t have to update the I539 form at this point.

Can i apply for f2 visa for my daughter and I in the same application form when my husband is on F1?

You need an I-539 if you are in the US and children are included with the parents application. If you are abroad and are applying for a visa...

Section 13 is a narrow category and its very difficult to obtain approvals. Still, we have no way of knowing the answer to this without reviewing...

I had my j1 canceled for shoplifting. Is it possible to get a J2 many years later?

unlikely, but be careful when you complete the visa application that you don't misrepresent any information. that could complicate things.