First time shoplifting under 1000$ while green card processing?

You must first work with an experienced criminal defense attorney and then will need guidance from an immigration attorney given waiver based...

The basis for the denial is generally provided and this should be reviewed to determine if refiling is advisable.

I'm 28 years old woman I got married to a 56 years old man 3 years ago we went for an interview but I only got a work permit?

Best to consult with an attorney to explore your options given previous history. Good luck.

Question for section 3 on i-485

Did you submit a completed DS260? If so, indicate yes. If not the answer would be no.

I131 form for a greencard holder?

Yes you should apply for the I131 and can have an attorney assist you with such.

It can take between 12-18 months for the I751 to be scheduled for interview or approved after biometrics.

More information is needed about her particular circumstances to understand if alternative options are available.

Will I be able to sponsor a K1 visa?

Unfortunately it appears you will need a cosignor.

Yes your documentation should be sufficient for travel.

Can I Apply for Citizenship If Divorced the Person Who Got Me My Green Card? I have 10 years greencard. I also hav a child ?

The divorce should not impact case as you are applying under the 5 year rule.