Yes, you criminal charge is potentially the cause of the rejection/denial. You should work with a criminal lawyer to clear that up.

His bar has long since been served, so he should be fine in that regard.

If your boyfriend is a US Citizen, the overstay should be ok. But why not get legally married earlier and file the paperwork while still in status?

Is there a minimum for ‘duration of stay’ granted when a change of status from F1 to B2 is filed?

You will likely have to file an extension of your visitor visa.

How does my I-485/GC impact with 1 count of misdemeanor in 2006?

Yes, it will have an impact. You should have attorney represent you at the interview.

If you are currently in the United States, it would be easier to get married and apply for a green and adjust status.

No, the online system often does contain complete or up to date information. Wait for the official notice by mail.

I would attend the appointment and bring both notices.

I missed my green card interview what should i do?

Call the I-800 number and ask for the interview to be rescheduled or request an infopass appointment to set the appointment at your local office. ...

How to immigrate to US as a convicted person?

It is unlikely you will be eligible to immigrate to the United States with multiple fraud convictions.