Hard to tell without having the file but...
-Did you apply a reset x-form to your meshes before doing the weights?
-Having all bones in the skin modifier won't be a problem, only the bones needed will be used
-When you copy the skin modifier make sure it's a copy and not an instance
-NEVER move the bones of the skeleton from their original position
(when you have to check weights by moving bones around, use angle snap, it will rotate by 5 degree increments, so it's easy to put them back into place)
Here's how to reset xform your meshes:
Read the first step.
EDIT: Instead of deleting the skin modifier on your cloned mesh, keep it, go in editable poly sub-object mode, select the portion of the mesh you want to detach, and then use "invert selected" and hit delete. Do this for each limb, remember to name each part correctly. Also remember to deselect any verts, edges or polygons you might have selected while in editable poly, if you leave a selection it "turns off" the skin modifier.