If the court orders require it, than yes. It should be encouraged as it shows the children that people can change.
If he has been established as the biological father you can not stop him from petition for visitation. That is his right as a parent. If he somehow is unfit you will have to prove that to the court.
Single father has no right to see his child until granted the right by a court. see link
One would assume the father has access rights and would figure out the child no longer resides with the mother. He will be notified that the child support will be going to a different receiver. see links below
If the father has joint-custody of the child, not many. You are also at risk of an accusation of child alienation if you refuse.
No he does not because he is not the child's parent anymore.
Yes, but he has up to six months to file an injunction requiring the child be returned. see long below
teens are only to see their family once in rehab
The right to petition the courts for the right to see and support his child.
Yes, unless he has been to court and has a order of visitation.
A father should always want to see his child, no matter what arrangements have been made. Whether it is being picked up or "delivered" a father has a right to see his child. On the other hand, if the parents are divorced or no longer together and the father has visitation rights he should not expect the mother to do all the transporting of their child. If mom and dad are no longer together then dad needs to accept his fair share of the responsibilities and not try to force more responsibility upon the mother by expecting her to deliver the child and the pick him up from visits with dad.
No, as the other child, even if a fraternal twin, can have a different father.
The two concepts are not related. Payment of child support is a financial responsibility. It does not depend on whether you see your children or not.