When is using magic to kill mortals (in self-defense) okay and goes unpunished in the later books? And your games aren't the books, so they aren't exactly a canon source. Also keep in mind that the game only goes up to Small Favor.
There are two parts of the Laws. The first part is the White Council's written law, allegedly scribed by the original Merlin. The second part is the metaphysical effect of breaking the Laws, the part that makes you a crazy monster, which happens regardless of the White Council's knowledge of you or vice-versa. Your... Idea, I suppose, that Harry just blames his anger issues on killing someone is also completely untrue. Harry Dresden has the First Lawbreaker power. It's in the rules, and we know how and why he did it.
Harry broke the First Law by killing Justin, and had to deal with the taint of black magic (and still has to, decades after he committed the act, in fact). And keep in mind, his reasons to kill Justin? Justin had the love of his life as a hostage, and was sending demons after Harry to hunt him down. He acted to save himself and Elaine. He was still a Lawbreaker, still tainted.
While yes, Harry can be an unreliable narrator, I honestly doubt the entire White Council is wrong on the Laws they've been enforcing for centuries.
And it's been explained how the Wardens take out warlocks. They shoot, behead, bludgeon, or otherwise kill them with weapons, not magic. They do use magic to defend themselves, weaken the enemy, and if possible hold them down to make the rest of the job easier.
You're also completely incorrect, Kemmler was not killed with magic. He was killed with a variety of weapons, including a flamethrower.
Finally, yes, mortal law is mutable. The Laws are more than that.
I dont recall anywhere where it was said he was killed with what you just mentioned. He was taken out by wizards i assume magic. He had a horde of things serving him so i assume they brought all their resources to bear, but to make sure he was dead and stayed that way..a spell would be my guess.
many people have argued the laws are more then mortal. I just don't see any real evidence that they are. Harry thinks they are; his enemies don't. Sometimes mortals are monsters too and they deserve the same treatment any monster gets.
I think Harry had problems before he killed Justin, I don't think it was the fact that he killed Justin. Harry is probably unstable from his upbrining and from what Justin did to him. Not the magic but the base betrayal it represented. Harry has never been in a good place. Fortunatly hes a good person. Its like Urial told him its his choice. he can choose to be a monster servant to mab or a human servant to mab. Humans are allowed almost universally the right of self defense in all ethical systems, it is considered moral to do so. Why would the laws of magic(if they are the wizards version of an ethical code) not be the same as all the other ethical systems out there. Essentillly you have a right to self defense unless your a wizard then you have to fight the mortals on their own ground with their best weapons. I dont think so. Buttttttt.
The real reason(my conjecture here) the laws are the way they are is when you violate them you strengthen the outsiders. That is reason enough to not violate the laws of magic and it is different from the "given" reason for violating the rules of magic. Somewhere along the way Merlin wrote the laws down because it was he who figured out what happened when you do. I bet prior to Merlin writing down the laws and enforcing them( and he could because his power was or is equal to that of one of the queens)(wiki) i bet people broke them whenever it suited them and it didnt do anything to them, except break down the walls between reality.Most wizards don't even know about the war with the outsiders. Wizards are human they get choice and free agency and that includes choice to use good things for bad. Execpt when wizards do it there are bigger consequences. I bet if enough wizards misuse magic things just slip in, no one notices it. Even the wizard who kills in self defense weakens the barrior. His individual act, one that he may only have had to do once in his entire life (not all live dresdens life) but its chink. Nothing happens to the wizard he was a good person doing a good act, but using the only tool he really has in a manner that does harm to boundries. He doesnt know it he will probably never know it.
I think merlin figured this out. I think its one of the reasons he built the prison wrote the laws, formed the council, its all a part of the war against the outsiders. And if he had to lie to make people follow it so what. The stakes are to high, at least he thought so.
You may say this is a quibble but its not, the given reason for breaking the laws of magic is it changes you into a monster more likely to get worse with each infraction. In story we have no real evidence of this. What we see is bad people using magic i n a way bad people would use it or any tool. In a self centered way theat benefits them.