Since she is not married to you and she has full custody yes, she can ask for it. if you are paying the bills you can ask for it to be reduced by the court though or ask her to drop it.
The mother should contact her (US) state child support agency. Be patient but persistent. Good luck!
Spousal support or alimony, possibly. Child support, no.
No. You will still have to pay child support for your children.
You don't. The mother's statement(s), even if false, does not relieve you of this obligation.
In such a case, the non-custodial father should prepare to begin paying child support.
In general, no.
generally speaking the only way to stop paying court ordered support is to go to court and get the order changed.
If the judge says so. Yes
The parent would get support from the children's father--only while the children are in her custody as minors.
Living on their own.
Contact an attorney.
As compared to what? Is the mother a child abuser? It depends on the circumstances.