Contact USCIS directly for guidance re: status.

Even if you did, it does not increase the timing for the visa to become available.

Yes it could but it depends on the nature of the charges. Consult with an attorney for guidance.

She must wait for the full five years before applying for Naturalization.

The USCIS webpage does not always reflect all processing times. Check back often as it should be resolved.

Yes, it would be best to re-file in the United States.

Yes, nicknames would be considered other names used.

Yes, as long as this is not in violation of the Adam Walsh act.

The US citizen may petition for the foreign national despite the felony.

A birth certificate should suffice for relationship evidence.