What is the I-1864A Contract between sponsor and household member used for exactly?

This form is routinely required in Applications for Adjustment of Status.

Citizenship

If we in removal proceeding, you need to answer yes and provide an explanation.

Your concern is well grounded. The US Consulates treat DWI and DUI's seriously in processing visa applications. I recommend you consult with the...

Can I quit my current H1B job sponsored by my employer while applying for marriage based green card?

The safest option is to maintain your H-1B status until your Application for Adjustment of Status is approved.

There are two parts to your question. The H-1B status of your brother has no bearing on your F1 visa application. Next, the timing of your visa...

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Is there anyway I can get a new interview or should I take a different course of action?

Failure to appear for interview may be a ground for denial. The most straight forward option may be to start over with a new adjustment of status...

Congratulations. That mean you are in F1 status now.

Since the misdemeanor: 1. occurred prior to age of 18 and 2. was dismissed, most likely, it will not affect the application.

What happens to illegal person who fights with roommate in NYC?

This depends on whether your friend will be charged an assault offense.

One of my family member is arrested with a shoplifting of 25$ .

One of the key rules with immigration filings is to be completely truthful. It's better to list the charge and include an explanation.