Child of unwed parents

If they split up, if they decide to create a custody agreement he can add to the agreement that the child cannot leave the state without his consent. On the flip-side that would mean if you wanted the child to come visit you, in FL they may not be able to without the mother's consent. But if the father got joint custody, you could visit the child while she was in his custody. You have every right to see the child too, but it may be difficult to get them to FL if they were to split up.

The best thing would be to get a court order that states his rights and hers. visitation, child support, tax yearsl, holidays would be layed out for them with what they agree upon with the mediator. the state the court order is placed in is very important. if they do split up he needs to file the paper work asap before she leaves the state with the child. this will allow her unable to move the child out of state to live without a court order. depending on the state you might want to check but i think either parent can take the child of state with no longer than 90days as long as it doesnt break any cout ordered visitation for the other parent. such as his weekend he could take the child down to see you.
(check with the courts if he would need something signed by the mother to do so). second you could ask the court for gandparent visitation

Me and my son's father were never married. he will be 2 years old in june and has had no contact with his father in 8 months. can I get him on abanonment? and what are his legal rights without a court order now?

I think you are getting ahead of yourself. If the parents are together I asume that they care for each other and their child. It does not matter if her mother wants her to move that does not mean she will. In any event this is a decition for the parents to make. In some states the grandparents have legal rights . However that can be exspence to pursue and at this point it does not look like this is an issue. What would make you think that if your son were to decide to move out of state with the mother of his child that they would not allow you to see your grandchild. Is your relationship not in good standing with your son and his girlfriend, if not then I would start working on the relationship. It is always best to get along if for know other reason for the sake of the child and the love of your child.