You have to settle this in court. But to answer your question unless the mother has comitted a crime then no.
Yes, the court will terminate child support.
In most cases, a mother cannot legally stop child support payments without a court order. Child support is typically mandated by a court and must be paid until the court modifies or terminates the order.
You don't, you fight it. Let me teach you how. see links below
If you aren't married and the mother has obtained a child support order then you must continue to pay until that order has been modified. However, it would be very unwise for the mother to allow the order to be modified since unmarried relationships are unstable and fleeting and it is difficult to obtain a child support order. She should be especially wary since you want to stop paying child support and charge your children rent to live with you. That's not a good sign.If you aren't married and the mother has obtained a child support order then you must continue to pay until that order has been modified. However, it would be very unwise for the mother to allow the order to be modified since unmarried relationships are unstable and fleeting and it is difficult to obtain a child support order. She should be especially wary since you want to stop paying child support and charge your children rent to live with you. That's not a good sign.If you aren't married and the mother has obtained a child support order then you must continue to pay until that order has been modified. However, it would be very unwise for the mother to allow the order to be modified since unmarried relationships are unstable and fleeting and it is difficult to obtain a child support order. She should be especially wary since you want to stop paying child support and charge your children rent to live with you. That's not a good sign.If you aren't married and the mother has obtained a child support order then you must continue to pay until that order has been modified. However, it would be very unwise for the mother to allow the order to be modified since unmarried relationships are unstable and fleeting and it is difficult to obtain a child support order. She should be especially wary since you want to stop paying child support and charge your children rent to live with you. That's not a good sign.
With approval of the court.
No. If the state is supporting the mother and child the mother has no right to free the father from his responsibility to support his own children. The state will pursue him for child support.
You need to return to the court that issued the order and follow its instructions.
It depends on the child support order and the age of the child. The rest is immaterial.
No. Support and visitation are separate issues.
Lawyer up. It's your only chance.
In a word, No.
No. You have remember that "support" is what the (usually) father pays the mother for the upkeep of the child. If the child moves out, the mother is no longer supporting the child and the father no longer needs to pay her.