... have to [pay] child support - yes, until/unless the child is adopted.
A noncustodial parent cannot sign his rights over to his parents or voluntarily terminate his parental rights. He needs the permission of the court and the custodial parent.
Not as long as it doesn't interfere with the access rights.
Legally, nothing. Morally, everything that that the mother has.
If there is no court mandated agreement that ensures the noncustodial parent visitation rights, then yes they can.
Only the court has the power to deny visitation rights.
Yes, if the court allows him too. He will still have to pay child support.
married or single?
See raleted queation
Unless visitation rights for the non-custodial parent were allowed in the divorce paperwork, the custodial parent is completely within their rights to deny the non-custodial parent visitation....however, the non-custodial parent may sue for visitation rights.