Is there any way to do some Mass edit so I do not have to create this new Event on every single unit?

You can edit a units parent and then right click on the item and click apply to children. This is a good reason to use a hierarchy when creating groups of new units.

What are "units parent"?

And is there a way to Set Opacity via triggers? Like, disabling that Actor Event until it is asked to get Enabled via trigger. It'd be nice for my new project.

Yes, you can create a behaviour to apply it. Create a behaviour (doesn't need to do anything) and then change the actor event from Actor Creation to something like Behaviour.BehaviourName.Created.

Objects in the data editor have parents, objects inherit the parent's values. The parent object for unit actors is GenericUnitBase, it is an object in the data editor like any other. To set an object's parent change the Based On value when you create the object.