Not necessarily answers, but some tips on how I would debug it personally. In scene mode, there is a little "mesh" button at the bottom that displays yellow triangles all over the mesh. This can be useful to see what parts of the puppet are moving and which are stuck. The points that are stuck can help narrow down where problems are happening. E.g. you can have an extra handle the looks harmless, but is causing that part of the puppet to be "stuck", causing unwanted warping. I often delete bits of the puppet then undo inside Ch just to see if that handle or behavior is the cause of the problem.
I would also look at how you have attached the meshes. Each time you put an independent crown on a layer (with the leading "+"), it starts a new "mesh". Each mesh has to attach to a parent mesh to follow it. You do that by dragging the origin handle of the root layer of a mesh over the parent mesh (so it turns green). Make sure "Attach To" is "Auto" as well. E.g. your neck artwork I think is part of the Head layer from the movements, which means you probably want the origin marker of the Head layer right at the bottom of the neck artwork, where it overlaps the Torso artwork.
I often think about this as each mesh like a new sheet of paper (or thin rubber sheeting) that you draw artwork on then cut out. You need the sheets of paper to overlap a bit so you can put pins through it to connect both bits of paper. Where you put the pin changes where the pivot etc occurs. I suspect this is your problem - you need to drag the origin marker for some of the layers to the right spot so the pivot occurs at the right spot.
Note: Personally, I normally include the Neck in the Torso layer if I want the head independent. That way the head pivots without the neck moving. If the neck is part of an independent head, then the neck is going to rotate with the Head. You can do that, but it might not give the look you want. Also note that if the character has a long neck, you may be able to get away with the head NOT being independent. Instead. you have the neck bend a bit has the head tilts.
Regarding hair behind the body, that is a problem if the head is independent and in front of the Torso (e.g. if the Neck is part of the Torso layer, so you need the Head in front of the Neck), but you want dangling hair behind the torso. If the head is not independent, there are no problems - its easy to get the hair to attach. If you want the head independent, you get this problem... which @k_oshiro just reported I think is fixed in the next CH beta. (I have not tried it yet.)