The visitor visa will remain valid and she can still travel using this.

No not if you are otherwise eligible for stimulus.

You should receive correspondence from NVC re: next steps.

Yes this is a very long time for processing, and is well outside normal. Best to consult with an attorney for guidance.

Yes this is okay and should not impact previously submitted and approved GC case.

Yes that should be sufficient to establish continuous residence.

No generally criminal record of petitioner should not impact case unless in violation of Adam Walsh act.

Yes USCIS should allow an infant to the room.

Yes an interview will still be required.

Yes this is viable for sponsorship.