"1) Atomic weapons …probably saved more lives/suffering than it consumed."
I take it then that you are a consequentialist: that you hold that no act is wrong in itself, but any act can be justified on the basis of its consequences.
(Is this your belief? If not, tell me what and why.)
If so, I would be interested in what sort of consequences count for you: is it a calculation of the number of human lives saved or ended, and that's all? Can this calculation have any cut-off point in time, or does it extend indefinitely?
Or do you, like the utilitarians, gauge "good" and "evil" by the increase or decrease of pleasure and pain? The promotion of an advanced civilization, and the suppression of a barbarous one? Or is it the kind of consequentialism that computes the number of people whose preference is satisfied by that action? Do moral and cultural consequences count, the suppression of depravity (e.g. Canaanites and their child sacrifices to Moloch, marriage by bride-capture, entertainment by pederasty) or the promotion of elevated values (the Reformation, Democracy, a Catholic realm for the Catholic monarchs, the Greater East Asia Co-Prosperity Sphere, the Workers’ Paradise?)
These aren't idle points, as I think that ordinary bad men usually only do a very moderate number of homicides and are satisfied with that. They're not consequentialists. But to rack up a truly large number of noncombatants killed, you generally have to be a "good" man or men: a government, or a religious movement, or a very, very high idealist, with a complete sense of justification that the good consequences outweighed regrettable but realistic expedients like "killing the innocent."
2) In order to understand the distinctions between murder and killing, one needs to understand legitimate authority and the justification in the use of deadly force."
Legitimate authority is one of the criteria which must be satisfied in the decision of entering into war, but it’s not the only one. The bombing of Pearl Harbor was clearly an act of aggression and justified the US House of Representatives making a declaration of war. Yet satisfying those two criteria for jus ad bellum (just cause and just authority at the outset) doesn’t mean that subsequently anything and everything is justified (jus in bello). What was justified at that point, was physically destroying Japan’s military forces.
(I think you have noticed that I am not arguing for pacifism here. Good. I am convinced that pacifism is a false doctrine, and also an extraordinarily harmful one: unusually harmful for a thing that sounds so noble.)
3) WWII … was total war…all elements of society are engaged.
I dispute that. Even if a regime is whipping up the total populace to make total war, it is in fact not so. In actual fact, many or even most people are still doing things which are unaggressive and morally blameless: the farmer farms, the mother mothers, the just man (as Hopkins says) justices: makes a distinction between good and evil.
It might be argued that sometimes it's devilishly hard to figure who and what is a military asset. Of course: every time you draw a line, there are some things that are borderline cases, and some things that are far to one side, or far to the other. But that is not an excuse for drawing no line at all. Normally, people act normally. (There's a good maxim.) And so normally, the wood-hauler is hauling wood,which he must do be there peace or war. If there are IED's hidden in the woodpile, all bets are off: blow 'em sky high. But to kill everyone in the countryside, or everyone in the city, by intent: that's murder.
Or if not, what is murder?
Begin with a different framework.
Instead of basing morality upon relative values, first identify the immutable.
There have been and always will be many, many, many deaths and casualties in warfare which are perfectly just, but never a consequence of individual judgment.
Likewise, God not only judges individually, He also judges groups. Hang around unrighteous groups and be prepared to suffer consequences which might never have been directed at a particular individual, but the unrighteous behavior of a group. That isn’t being indiscriminate, but rather discriminate on a different scale.
A flash mob might think they won’t be held accountable, but when deadly force is applied to that size of group, it is likely many kids who joined in on a lark may find themselves in a slaughter.
Murder is a crime against the State and God. Use of deadly force to defend the State or the just and righteous immutable laws of God when they are threatened by the unrighteous is not murder, although legitimate killing may occur. This is only one of many good reasons to remain in fellowship with God, to study His Word, and meditate upon His Word. Without that obedience, then relative morality becomes the norm, which is no better than the worst immoral action.