Are custody agreements required?

I was granted emergency custody and then temporary full custody order.

We failed at mandatory mediation to come up with an agreement. We are now
divorced. There are no terms in our separation agreement regarding custody or child support.

Our first custody hearing is scheduled in October. Can I drop
the custody case on my own without need for her conscent to do so?

If I can not drop custody case on my own can we both drop the case?

Does there need to be some form of custody support or agreement filed in place to drop it?

A party can dismiss a claim at any time- doing so does not drop the other side’s counterclaim if there are claims pending, and it will not cause a continuation of schedule hearings. You don’t have to have any agreements in place to drop it.

So custody agreements or custody orders are not ever requried by the state?

Parents with children can divorce with no required custody agreement or custody order ever to
be in place?

They are not required. However, most parties nowadays do work out an agreement or have an order put in place regarding custody. If the divorce happens and neither party signs an agreement, nor files for custody, then there is no custody order or agreement. Both parents have technically equal rights to the children in that case. Either one of them however can file at any time for full or joint custody.