It seems like it's one sun per shot. Anyway, it's not a very good weapon. The Death Star had a reactor that powered its self. All the Rebels need to do is live on a planet like Pluto, or the equivalent.
It seemed to me that this weapon shot across the galaxy. No hiding from it at all.
It does, not exactly that but similar to shooting through hyperspace. The techno mumbo jumbo is explained in the novelization, though only in part, as the Resistance scientists were guessing, thought that what Finn heard about it was largely impossible, that some features made no sense scientifically or wondered how the First Order could even acquire or develop such technological advances out of reach for the Republic).
This could just be the novel trying to cover up what some could see as a "plot hole", or maybe it's a clue about allies of the First Order we don't yet know about. The First Order hid itself in unchartered zones of the galaxy.