If you've been convicted of a felony since you received (or last renewed) your green card, your permanent residency could be at risk when you next renew.
Immigrants can obtain permanent resident status through marriage to either a U.S. citizen or green card holder, but the rules are a little different in each case.
Depending on where you are in the application process to become a legal permanent resident based on marriage, an annulment of that marriage may present some complications.