1. Exactly - the order of layers controls what is in front of what. So yes, move the eyes to the top is fine and normal. Just keep under the same parent. Behaviors do not care about the order of children etc (err, 99.9% of the time). Eventually you might hit an annoying advanced cases where "oh, I want in front of that and behind that but the parent layers don't allow that". Things to look forward to! 😉
2. I would do some tutorials on independence etc. If you want hair to be "independent", which I often do so it can bounce around etc, then it has to be "attached" to a parent layer so it moves with it. Normally Hair will be inside Head so the hair will follow the head. I might create a "Hair Fringe" layer in front, make it independent, add some dangles so it bounces around, then change the "origin marker" of the fringe layer to control where on the head it attaches to. A common mistake is to go wild on independent layers. Don't! Add it whenever you want something to move independent to the other artwork. E.g. hair wants to move separate to the face (if long hair or a fringe). But the face skin artwork rarely would be independent - it should be part of the Head.
(deep breath). Why? Because Ch has the concept of "meshes". When you mark a layer as independent, it starts a new mesh. Think of it like a new sheet of paper or thin rubber you draw on. You can stretch that sheet as needed, and it will only affect the artwork drawn on that layer. But you want to attach it with a pin ("hinge attachment") or staple ("weld attachement") which will control how it moves relative to its parent. Your fringe should be attached at the middle/top of the fringe artwork, so it moves with the head.
So there is a clear tree of nested layers - very important for behaviors. There is ALSO a tree of meshes. Children meshes attach to parent meshes. If the Face skin artwork, for example, was independent, you can end up with the "Head" layer with no artwork in its mesh (if all children are independent). That means there is nothing for the children to attach to! So Head generally has the face skin layer not independent, then eyes etc can attach to it.
When you click on a layer, you will see a yellow outline. That is the mesh outline for all artwork in that mesh.
But go watch a video - probably will explain it better.