Consult with a business transactional attorney.

You must be careful with respect to timing, or may have to leave the US to obtain the F-1 visa anyway.

Sponsoring Immigrant Parents

Generally, the petitioner's criminal record is not the subject of inquiry in most family-based cases.

Failure to disclose drug conviction at time of registry

If he was inadmissible due to a drug crime, then his green card would be invalid. he should consult with an attorney.

Yes, changes in employment can always have implications. Consult with the attorney representing you and your company regarding these questions.

How can I still come back to USA with the approved PERM by resigning company A.The chances to come to US are active still or not

You cannot back to the US based solely on an approved PERM or I-140.

You were ten-printed if the government took images of all ten of your fingerprints.

How can I appeal my husband's visa denial at CDJ,MX?

This can be a problem and usually an applicant who is refused on this basis must wait a much longer period to reapply.

Will this judgment interfere with her/our adjustment of status to Green Card? Can this be considered crimes of moral turpitude?

Immigration fraud is a big problem when seeking future immigration benefits.

Naturalization exempt

She is not qualified for an exemption from the English language requirement based on the facts presented.