The battery trick is just short the 2 heater leads together and just stomp anode/heater across a car battery - if you're lucky its only a loose flake of cathode coating and it'll just be blown away without damaging the heater. If you're not lucky, the magnetron will just be slightly more dead than you started off with.
The epoxy around the heater lugs sometimes has voids in it, it doesn't necessarily mean a fault. If the epoxy is cracked or scorched, the feed through capacitors may have broken down, The metal box on the side contains a pair of thick wire chokes in series with the heater tails, those with the potted feed through capacitors form a LPF that stops the RF escaping via the heater circuit.
