Consult with an attorney for guidance re: your case.

Yes you may apply for N400 while the I751 is pending.

Contact USCIS and request GC be corrected.

No not without status. Consult with an attorney for guidance.

Yes that should be sufficient to fulfill requirements.

This should not impact your ability to petition for your Fiance.

Depends on if you previously applied for the same visa.

This is very common unfortunately and should expect delays.

No that should not impact a future citizenship application.

A certified copy of the criminal records is needed.