If a mother and father are unmarried and have not yet settled custody of child can the father get up and walk away with child during visit?

If there are no court orders in place, he could walk away with the child.  If you then called the police, depending on the circumstances, the police may return the child to you (i.e., if the child is very young and it is clear to the police that the child has been living with you).  You should file an action under the Uniform Parentage Act (the body of law that governs unmarried parents) to seek a custody order.