Do you have to pay child support if the child is home schooled?
Yes, but you most likely don't have to pay the difference between home schooled and public school.
Do you have to pay child support to the mother if the child has been voluntarily placed by her in a group home?
You would need to return to court to do so, and it's likely the court would simply order your payments to be redirected.
When a child is abandoned by a parent receiving child support how does that child get the child support?
The persons in custody of the child must file for legal guardianship and request the court modify the child support order. The person needs legal standing to receive child support.
Do you have to pay child support if you give up your parental rights to a child if the child is living with the other parent?
Usually you have to continue pay even if you give up your parental rights, yes, unless the other parent agrees to you not paying anymore.
Do you have to pay child support if the mother is in prison and the grand parents have the child and won't let you see the child?
Yes. But don't send the money to the grandparents - send it to the courts or the State disbursement unit. You may go to court to require the grandparents to grant visitation.