When I rotate a bone in pose mode, it changes the dimensions as well. Is this normal? How do I prevent this? Does it have to do with the dimensions or the scale I have for the bone?
I'm not sure why you have several armatures with one bone each time rather than one armature with several bones. That said your stretching problem comes from the fact that your armatures are not proportionally scaled, select the one you want and press CtrlA (Apply) > Scale: