Which marriage date should I put on my I-130?

You should put the date of your Korean marriage.

How to prove to husband's supervisor that he needs to stay with me based on immigration rule?

There is nothing in immigration law to assist you. I am sorry.

The day of interview

That should not impact the interview. You will need to bring originals of your birth and marriage certificates.

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Any guesses f2a priority date 08/28/2013 would be current. Just a guess. This is a visa regression case for the rest of world.

It is impossible to predict when your PD will be current. If you are in the US, it is important to remain in lawful status while you wait.

Green Card expires in 6 months, I'm moving to another state in 3.5 months. Should I wait and file I-90 in my new state?

The most important thing to do is to file an AR 11 after you move. If you are moving soon it is probably best to wait until you move.

What should be my next step for my husband to get his green card here in the US?

Unfortunately, he will have to go back to his country to obtain his green card.

I lost my passport and had to go to my embassy to get a new one , how do i get a replacement 1-94 .. i recently got married and

You can file a form I-102 to obtain a replacement I-94.

Is it possible to obtain permanent residency through marriage?

You may be eligible for a green card but it would be a complicated process given that you entered the country illegally. Did you apply for DACA. It...

Can i apply for green card through my citizen brother while i am currently in withholding of removable status.

Your brother may be able to petition for you but you should know that it takes at least a decade for you to be eligible for the green card.

WHAT IS NEXT AFTER A MARRIAGE INTERVIEW?

If you entered the country illegally that may be a basis for a denial of your application. You should consult an immigration attorney as soon as...