USCIS will request an RFE if more information is needed to process your case about mid-way through the process.

It depends on the type of work visa and if otherwise eligible.

Best to have your retained counsel explain your case as s/he knows best.

Yes you submit a case inquiry if case outside of processing.

Yes you should be able to travel to your home country under your GC category.

It can take many months before card is issued.

Contact USCIS directly to inquire about request.

Your mother may apply for a tourist visa on her own if eligible. Consult with an attorney for guidance with process.

More information is needed about the underlying inadmissibility and waiver. Consult with an attorney for guidance.

Did you file a fee waiver with this? If so, that fee was waived.