Legal Question in Family Law in Florida

No -but because you two have agreed you can use it in court when you appear before a judge for the purposes of straightening out a custody/support issue. Then it will become a part of the pleadings.

Yes, it's still a binding contract so long as both sides have signed it. However, in order for either side to seek sanctions for contempt of court, it would have to be filed and a judge would have to enter an order (or a divorce judgment) ratifying it.