You may depart without issue with your valid forms of identification.

She may file the I485 90 days post entry as long as her intention was sound.

Yes you should resubmit with cover letter.

Yes you may petition her despite your criminal record.

This shouldn’t be an issue and you can inform officer at time of interview.

Best to work with an attorney to prepare for interview. Good luck!

Use your full legal name for signature purposes.

Your full criminal history must be reviewed to provide appropriate guidance.

Best to have your retained counsel review your case and provide guidance.

No this would not be a basis to obtain a visa.