That's selective according to individual state laws
If you live in the US... The father's parents have no rights to custody at all. The father has the right to petition for custody, but he won't be given sole custody unless he can prove the mother unfit. He might, however, be given joint custody.
the father gets the custody of the child if the mother dies
The mother. If she dies, her parents get custody.
The mother assumes automatic custody, unless she is unfit.
I believe that the mother should get custody and she gives the father a schedule to be on.
Yes. The child is your baby. As long as your a fit mother the child cannot be taken away from you. If you are a minor, your parents still have custody of you, but you have custody of your child.
mother has sole custody even if living with father
The mother. The father have to petition the court for custody or visitation right.
That depends on why the mother lost custody in the first place. The court must have granted the grandparents custody for some reason. If they have custody now you have to apply in court for the custody to be moved.
The mother is presumed to have custody unless there is a court order saying otherwise.
Mother has sole custody in every state except Arizona. see link below
Since there is no court order and you were never married it is the mother that have custody. He can be charged with kidnapping.