Can someone help me understand prefabs?

It definitely is possible to drag a prefab into a scene to create instances of it, which retain connection to the prefab so that edits to the prefab impact on the instances (unless you've overridden properties in the scene instance). But this only works at edit time - if you create instances of prefab at run-time they're just clones of the prefab with no connection to it. So it sounds like maybe that's what you're doing...?

For me, the key thing to understanding prefabs is that a prefab is simply a text file providing a recipe for creating a game object. And a scene is a text file providing a recipe for constructing a scene A scene's text file can contain a section saying "make an object using recipe X". The section can also specify overrides for values inherited from the prefab's recipe (so then it becomes "make an object using recipe X then change these values"). And so if you change the prefab file, anything that you change gets changed in all the objects made from it. BUT... all that is edit-time stuff. As soon as you press Play in the editor, or run the scene in a build, those objects are created according to the recipes-with-overrides and from that point on they're just independent objects.

If the above doesn't help I think maybe you need to provide more detail about what you're doing. Edit time? Run time? How are you "editing the prefab"? What do you mean by "add the prefab to the hierarchy or scene"? And so on. Also note that the hierarchy is just a representation of what's in the scene, so that last quote confuses me a little)