Yes, you can file the Green Card petition without her updated documents that reflect the new last name.

Yes, you can filed a lawsuit (mandamus petition) against USCIS. Seek an immigration attorney’s advice to assist you with the lawsuit.

Assuming the USC child is 21+ years old, they can sponsor the mother who overstayed as long as she entered the US legally. I-130 and I-485 can be...

The current processing time for VAWA is 30.5 months.

Yes, you may receive two paychecks simultaneously after being laid off by the previous employer.

Follow this document checklist: https://www.uscis.gov/sites/default/files/document/forms/attachments.pdf

Yes, mailing documents to embassies is permitted. Ensure you have the right address before mailing your documents.

An H4 beneficiary can stay in the US while the H1b spouse is travelling internationally for a temporary period of time.

I suggest that you retain the services of a New Jersey licensed attorney to file a motion to reopen your case. You'll have to address that issue...

Yes, an F1 visa holder can work for a US company from his/her home country.