NC will remain the jurisdiction state (in case either of us move back it would make things easier)
If you move outside of NC, NC will no longer have jurisdiction over the case as the mother and children have previously left the state. Jurisdiction will be in the state where the children now live.
I cannot make a determination of what a reasonable schedule for your children would be.
I think your proposal regarding travel expenses and uninsured medical expenses is reasonable.
You cannot relinquish your parental rights. Your ex would have to make a motion to have your rights terminated, and the court would decide if a termination of your rights was in the children’s best interests.