Someone just really likes to force push the hornet's nest.
Chaotic and psychopathic killer? That's a bit out there for even me. Mass murderer maybe. Because I'm going to say that the average non-military people on the Death Star didn't deserve to die. They were just trying to make a living, support themselves and their families, and generally be on the "not being oppressed by the Empire" end of things. I can't blame them. These people aren't going to sign up for the Stormtrooper Corps or Imperial Navy, but they'll make a living doing their dry cleaning.
Here's the thing, we're really asking two separate questions, "Did the Death Star need to be destroyed?" and "Did everyone on the Death Star need to be killed?"
In war, is the killing of an enemy soldier murder? (My opinion is no, given that both sides signed up to fight for/defend their side, and since the other guy is trying to kill you right back, one could argue for self-defense.) What about innocent civilians? Are there such things? I cannot think of a single non-military occupation that I could not argue would contribute in some way to a war effort. If someone else can, let me know, I'm not saying there aren't any (but I don't think there are), just that I cannot think of one.
Did the Death Star need to be destroyed? Well, if you were on the Rebellion's side, very much yes. If you were on the side, fighting or not, that didn't like the Empire, then yes. If you believed in the law, order, and stability that the Empire represented (and there were places where the Empire's presence made things better, at least until the rebels showed up and started blowing things up), then having a giant super-weapon battle station the size of a moon was a great thing. Ain't nobody gonna make any trouble with that around. At least until it became a target.
Is Luke a psychopath? In my opinion, no. A mass murdering terrorist who hears voices, talks to ghosts and little green men, and subscribes to an ancient mystical quasi-religious order whose motto appears to be "We're the good guys even though every few hundred years or so some of our order splits off and turns evil and eventually seriously messes up the galaxy." (I imagine a sign somewhere in the main Jedi temple: "
182 3 0 years since last fallen Jedi" (because Dooku and then Anakin) (<-note: I just made up the 182 number for amusement. I have no idea how long it was before Dooku left that a Jedi saw the Dark and turned).
Did the Death Star need to be destroyed? Depends on which side you were on. But I'm going to say probably, but only because of how blowing up planets can muck up hyperspace lanes.
Were the Rebellion's actions justified? Well, from their point of view, yes. But I think the average worker on the Death Star would have at least liked to have had some warning and a chance to evacuate. Heck, I think most Stormtroopers would have preferred the option of being allowed to leave the Death Star before it was destroyed, even if it meant they became prisoners of the Rebels.