I don't know about "abandonment." Parenting time is his right and he has chosen freely not to exercise that right. I don't know if that is legally considered "abandonment." You might want to talk to your attorney about having his visitation reduced or eliminated or supervised or in some other way modified because he hasn't had cophysical contact in over a year and the child, depending upon the child's age, may not be comfortable with him at this point. Or you can do nothing and hope he either decides to become a propoer Daddy or stays away. In other words, you hope he maintains consistency, so the child doesn't have to be confused and repeatedly hurt.
The CS is another issue. You can certainly deal with the CS issue. Go to the Child Support Enforcement agency in the jurisdiction where the CS order was filed and have them enforce the order. They can do this through wage garnishment, pulling tax refunds, etc. They have their methods, but you have to let them know he hasn't been paying.
One caution: Don't be surprised if, when CSE finds him and begins "punishing" him and/or taking the required support by whatever means necessary, he all of a sudden shows up and takes an interest in exercising those visitation rights!
