Should I file i-864 for my husband with my new name( Changed last name) or previous name?

You should apply under you current legal nae.

Immediate relative only applies to spouse parent or child of a US citizen. Your granddaughter will be eligible as a derivative of your daughter.

Filing i130

Most crimes, but not all, do not prevent a petition. You need to check with the particular state as to requirements for state ID.

Does my H4 visa needs a change?

You H-4 is dependent on you spouse's H-1B. As long as your spouse maintains H-1B you will be able to maintain H-4.

K-1 visa interview was approved on may 21 , but my visa status still AP ?

A month is a bit longer than usual. Contact the consulate.

Can I stay longer in my tourist visa if I sent already the paperwork?

You do not indicate what paperwork you submitted. In general a properly file petition and application permits a person to remain while it is pending.

Can I enter using old visa and new H1b receipt (using AC21)?

Follow the guidance of your attorney and if the company has an immigration attorney the company's immigration attorney will provide proper advice.

Can I stay in the US while I wait?

You may remain with a properly filed visa petition and adjustment of status application

Yes to you and your spouse is a derivative of yours that is how she adjusts. Consider having advance parole before traveling.

Naturalization certificate?

You can try a FOIA/PA for your file and there may be a copy in it., although not likely. if you know the court where he was naturalized you can...

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