The hot battery bus runs items that may need power while you are not there. On the -400 it runs things like the dome light, refuel/defuel panel, aft baggage light boarding lights and a few other items. All the hot battery bus items are connected directly to that bus which is powered by the standby battery.

The lav is exactly as described but there is NO indication in the cockpit.

Cargo fired...lost me on the hatch part and extinguisher. We are talking about different variants of the dash 8 so unfortunately some of this may not apply.