ex want to have a child custody agreement via solicitors and want to make it legal binding. first question is "can custody agreement between solicitors become legal binding"?
second question is "can I add child maintenance payment on that custody agreement"?
An agreement between 2 people isn't legally binding, I would think your ex is referring to a Child Arrangements Order made by consent between the two of you. This would be legally binding and court enforceable should either party breach a clause in the order.
The Child Arrangements Order doesn't usually include details of child support, if you can't agree on that between you then either parent can make a claim through the child maintenance Service.