Concerning the old steel BX cable. It did not have a bonding strip to bond the steel jacket together. Electrically you would have the conductors inside a coil. Fault current would follow the circular jacket and end up getting red hot while the impedence would not allow it to trip the breaker or blow a fuse.
This problem was the basis of the restriction to six feet for armor flex when used for grounding. The six feet of conductor length would have over 18 feet of return path on the steel jacket.
The Copper conductors are good compared to the resistance of steel.
I would recommend GFI receptacles rather than trusting the BX. For the fridge you may have to just pull a new circuit.
