You can notify USCIS of the error at naturalization time.

Best to have an attorney review your case to make such determination.

Yes this appears possible based on information provided.

It appears the answer would be affirmative.

You will need a new F1 but no issue with unlawful presence.

You will receive an RFE, not a denial based on information provided.

It depends on the specifics of the case. Consult with an attorney for guidance.

You should indicate yes based on information provided.

If submitted you should wait for response from USCIS.

You would be eligible after 5 years.