Here’s what I found:
“Can I get an annulment?
Generally the answer to this question is no. Annulments are available only in limited circumstances in North Carolina. These circumstances include all marriages between any two persons nearer of kin than first cousins, between double first cousins, between persons either of whom is under sixteen years of age, between persons either of whom has a spouse living at the time of the marriage, between persons either of whom is at the time physically impotent, or between persons either of whom is at the time incapable of understanding the marriage vows. Additionally, a marriage contracted under the belief that the wife is pregnant, followed by the separation of the parties within 45 days of the marriage, which separation was continuous for a period of one year, shall be annulled unless a child was born to the parties within ten months of the date of separation.”
As to the first part: “No, the separation agreement does not need to be filed with the courts for it to be a binding contract.”