The question is does a serial killer have the Din of a Rodeif.”
Of COURSE he is a rodeif. He already killed several people. Why would you think twice about killing to defend yourself? BUT – he would have to be coming toward me even after I would have warned him to back off, first. Even without a convenional weapon, many serial killers, murder with their bare hands. In that scenario, and assuming I knew how to shoot the gun and not accidentally kill MYSELF, I wouldn’t hesitate even one second to shoot. Hashem should spare us all from ever being tested in such a gruesome manner.