How do i organize and group objects and their blueprints?

In the BP, you can Set Visibility separately for every component.

And yes, you can select a separate component in the Viewport. To do so, you have to either find the component above the details to the right of your window when your BP is selected in the Viewport, or just double-click the component in the viewport itself. But since you need to switch visibility on/off at the runtime, you have to create those functions in the BP.