My problem: everything works in the Unity Editor, Dialogue System is connected, everything is fine. But in the build itself, Dialogue System...disappears? And when I built the scene without Menu framework, everything worked.
Have you tried playing in the editor from the first scene in build settings?
Make sure your first scene in build settings has a Dialogue Manager configured the way you want. If you have a separate GameObject with a Save System component, your Dialogue Manager should not have a Save System component.
A quest log came with the framework menu. But since I already had a quest log, I disabled this tab in the menu and pause. But yes, on the button "J" calls both: my journal and the journal from the framework menu. I couldn’t find where to disable his call by button.
Check the Dialogue Manager. It may have a quest log window GameObject in its hierarchy as well as a quest log window prefab assigned to its Instantiate Prefabs component's Prefabs list. Remove one or the other.