STBX Abandoned Home

My wife and I had custody arrangements(court order) for our son once we lived in separate homes. We also had a consent order that stated that she would be responsible for some of the mortgage as long as she lived in the home with me. However, I could never get her to sign any kind of agreeement concerning how she and I were to conduct ourselves while living apart. I came home in April and she had moved out without my advance knowledge. My question is are we now considered legally separated? We have no intentions of ever coming back together. Can I date? I consider what she done to be abandonment since we never could get a signed separation agreement in place.

Yes, once the parties begin living in separate residences they are legally separated.
I always advise folks not to date until a formal separation agreement is in place, as it can heighten emotions and make negotiating more difficult. Further, any relationship you begin after separation could create an inference on the part of your ex that you were involved with this person prior to your separation. Also keep in mind that the act of sexual intercourse (adultery) is still a crime in North Carolina, and until your are divorced having sex with another aside from your spouse is adultery.