Okay, i only read through the first page, so I'm not sure if someone has said this, but i don't think so from what I could see.
My answer is sort of partly from a legal standpoint. I'm a law student and I can't help it after studying murder so much recently. I'm not sure about anywhere in the US, but in Queensland (Australia) we have the
Criminal Code (Qld). There are a few sections that the elements of murder come under, one of them being s291
Killing of a human being unlawful
It is unlawful to kill any person unless such killing is authorised or justified or excused by law.
I suppose that you could say that, in terms of Faith and Buffy killing himans, that it is justified or excused by law if you could find a section that worked. And, if they had killed the mayor before his demonness, you probably could use the partial defence of provocation. I can't copy that here because the copy of the code that I have here is outdated and I'm too lazy to find an updated one, but you could most definitely prove that they had been provoked, even just by mere words as, in this case, they are of an extreme nature.
You could also go by self-defence in the above scenario, and defence of another. So, while it is a little bit of a grey area morally, from a legal standpoint it could be justified, and not even obliquely. Of course, that's in Queensland, but I presume there are similar provisions elsewhere.
Where was I... oh right, moral grey area... it is a moral grey area and I don't think Buffy could live with herself if it happened. I don't think I would feel the same way either and I still think it would be wrong, but I can see that they would have had a legal, and in a way moral, justification.
But i'm glad they didn't
There are other sections for murder, and they all add to the offence, but basically, it's not murder unless it is a human being (and obviously that comes into play with the whole abortion thing... when is a person a person... but let's not get off track

)
So for me, when they kill demons, I don't see it as bad. Well, that's not true, in some cases I do, but when they kill demons, I don't see it as murder. For me, murder is only when a human being is killed.
That said, someone mentioned demons like Clem before, and I would be distraught if Buffy killed Clem (btw I'm glad to see him in season 8

). And for 'part demons', I suppose that's tricky. This is more into Angel, but Connor (well technically he's 100% demon

) and Doyle, but that get's really complicated.
And I know its not really my opinion, but after spending so many hours pouring over case law recently I cn't help it.
I don't really think the slayer should be above the law. Buffy certainly doesn't see it that way (I mean, her reaction shows that, and her reaction in Ted).Faith sees it the other way round. And I don't think that the end justifies the means (ie: don't go killing the mayor while human sort of thing), but where she's damaged public property, that's sort of in the course of duty, and while it's wrong, to an extent i don't mind so much. And most of the damage she does is in her own home anyway, apart from the whole blowing up the school thing, but that's okay

Woot, back to study