If the mother and I agreed to a one time lump sum child support payment can she change her mind later if it's legally documented
Depends on the agreement. One thing is certain, the likelihood of a court upholding an agreement that substantially reduces the amount of child support that the custodial parent should receive by law is slim to none.
yes, best interests of child controls.
It would depend. How old is the child and is there any likelihood that you and her would earn more income in the future as child support is based on the income of the parties.
You cannot really bargain away child support. If you are talking about arrears then yes you can arrange for a lump sum payment to erase the whole thing.