well i tried to find some pictures to explain how to tell if it is cable or hydro but i am having no luck with that... so on to your other questions... there is no way to tell if it is in good shape unless you take it apart... as far as the diff... if you look where the axels go in, if you can see strait threw to the other side with NOTHING in the way it is an LSD, if there is a bar in the way then it is an open diff...
-Keith