Crumbly insulation at any point means replace the wire. You can't see most of it and if what you can see is degraded there's a good chance it can be degraded too.

BX shield can form a ground, but is no longer permitted to be used that way because at best it is not a good ground connection. If the runs and bends allow it, you might be able to pull new conductors (of the correct type) through the shield instead of opening the walls; just include a ground wire too and you should be good to go. Normal wire-pulling techniques are not easy doing this in such a small diameter space and you need to ensure that the insulation isn't being damaged by sharp edges on the way in- have a helper watch and feed the new wires as you pull and install grommets where needed.