Those circumstances do not give the father rites of custody. The courts grant rights to custody based on the safest and most conducive environment for the children, with a traditional bias toward custody for mothers.
Sadly, trying to prove one or the other is the betterparent is a pointless endeavor. The adversarial nature of US courts is such that one parent must prove the other is less than fit or unfit, and THAT is not a conducive environment for children.
none except standardized visitation.
Yes, if the father is not given custody he will be obligated to keep paying support to whomever the court awards custody or guardianship of the children.
yes
My answer to that would be 'No'. The father is responsible for providing child-support regardless of who has custody of the child; at least until the age of 18.
How does he have any visitation rights with a custody and child support order?
You may have to pay child support to the one who has custody of your children.
If you're the father
yes
Yes he can. The court will award full custody to the mother or to a legal guardian if necessary. However, the father will be required to pay child support.
No. If there's a court order against the father, which resulted in any kind of arrears, the father is still responsible for it. Arrears are paid and there's no statute of limitations on it, as well as, any support and/or custody modifications.
No, if the mother voluntarily gives cutody to someone else, she can no longer be paid child support because she no longer has custody of the child. What happens now is the father can obtain custody because he does have rights or the person who has custody and have legal guardianship can file for assistance in which child support can be included or filed.
If he has them and refuses to return them you can call the police. If you want him to have legal physical custody the both of you need to go back to court and have the custody order modified and the father's child support order terminated.