You should discuss with your attorney for case specific inquires as he is best suited to answer these questions.

Green card petition for mother

The cover sheet also has a section that says "not available" or "not applicable." You would indicate accordingly. She needs a police certificate...

Am i legal to go back to the USA?

No based on your fact pattern you would have a difficult time obtaining a subsequent visa without the appropriate waiver.

I-130 Approved Pending a Joint Sponsor I can't find

The requirement cannot be waived and you must either find a cosignor or use your husbands assets when they meet the minimum requirement to fulfill...

Should I change my name now or after I get my citizenship?

If now you must go through your state court and petition for a name change. Otherwise you can wait until you are eligible for naturalization and...

Likely not but a full review of your criminal history should be made for a better assessment. Consider consulting with an attorney for assistance.

Immigration ?

You should notify USCIS of the pending divorce in order to waive the joint filing requirement. Further you should obtain an extension with your...

K1 Medical Exam?

No, a hair sample test is not included as part of the medical exam but you can inquire with the designated medical site for confirmation.

You are no longer in F1 status and should depart the US right away as to not accrue any unlawful presence.

Question about i130, i485 or counselor processing or i539 for extension of stay.

They should file Form I485 to adjust their status in the US now, or if they have not accrued more than 180 days of unlawful status can complete the...