I have a green card based on asylum application. Can I travel to Mexico without having advance parole?

You do not anything to travel except your green card and a current passport.

Do I need to apply for I-131 for reentry to US form Canada. I already have a green card.

I must disagree with the previous answers. If you are in school in Canada, have family and other ties to the US and entry the US every six months...

You do not need to cancel or do anything. By leaving the employer that "cancel" the visa and status. Unless, of course you want to go back them...

Is it a requirement to be working (physically present) in the state where the E-Verify company resides with an OPT STEM?

You need to be on payroll and be an employee in S Carolina but you can actually work in Houston if they have a formal agreement between the two...

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Immigration question

You must execute an affidavit of support regardless of your income and you probably will need a co-sponsor or rely on your husband's income.

Can i authorise another person to perform official wedding on my behalf when the girl is in kenya and i am a usa citizen

proxy marriages are not favored and are difficult to assess without information about local law. You need to consult with an immigration attorney.

There are lots of Board Certified immigration attorneys in Texas in general and El Paso in particular who can help you immediately. Just google...

I have TPS only married to a US citizen

You need to take all of your criminal records and immigration records to a qualified immigration attorney immediately.

When can I carry over my priority date for the future cases? My green card has submitted under an EB-3.

The EB-3 PD will only carry forward if the EB-3 I-140 is approved.

How can i help my boyfriend who is currently hold with ice n is sentenced to 6 months then deported?

What you need to do is get all of his criminal and immigration records and go see a qualified immigration attorney. Immediately.