What if the parent signs their rights over and the other parent signs the paper that the child support is to stop.Will a jude allow that?

No. Signing the rights over; terminating the parental rights does not eliminate paying child support.

Now maybe you have some deal going, I do not know. Is the child support court ordered? You have to go back to the courts with your plan and I highly doubt a Judge would allow this. Child support is FOR the child's welfare and education and personal needs.

Not normally, the judge is looking for the welfare of the child, and normally believes that the child will need and should have the support.
Next esp if the custody parent or child is collecting state welfare or the judge believes they could, they want the non custody parent still held responsible for some repayment.

What has to happen to even try this, is to go to court with motions to modify any existing orders, if no orders in place, you have to file in court for court ordered support, custody and more

If you read the other threads on this issue your question would have been answered. A judge is not likely to allow you to terminate in the first place. They are especially not likely to deprive the child of a means of support.

No.

They want someone to be financially responsible for the child. The taxpayers don't want to raise the child. That is the parents responsibility.

First off, parental rights can't just be relinquished unless someone is willing to adopt... so you won't even get past the first step anyhow.