The narration says that the Grim Reaper was formed out of sub-conscious (and conscious) fear of death in living things. If death, the state of being, existed independently of Death, the Anthropomorphic Personification, why did things stop dying once Death was fired? Shouldn't things go back to the way things were before Death came into being?
Because even if Death wasn't originally needed for death to occur, he's in charge of it now. It's like any petty government function—completely superfluous at first, over time it becomes vital because people forget how to go without it.
I think Death came into existence before anything actually died- as soon as the first organisms thought about the concept of ceasing to exist, Death appeared. So there was no time when things were dying that Death wasn't around. Well, maybe a very small delay while one organism wondered why the other had stopped moving. But once the concept existed, so did the personification. He probably wasn't the complex personality we know now back then though.
Or maybe he was. Remember that the first non-divine living organisms to appear on Discworld's surface were Rincewind and Eric, and one of those two ALWAYS has the possibility of his own demise in mind.
Belief has been shown to retroactively change reality on the Discworld, so that once Death came into being, he had always been there.
It was mentioned at some point that Death always existed, but for millennia just performed its function blindly. But eventually, life rubbed off on Death and a personality coalesced. He became curious about the creatures he was reaping, and created his domain in imitation.
This makes sense, as the ongoing rubbing-off process is very noticeable over the course of the series. This troper thinks Death first became a sympathetic character about the same time he started to swear.
Actually, it's just humans who don't go away, everything else just conjured up their own deaths again, which is where the death of rats came from.
Also , it was mentioned that destroyed objects leave a ghost behind, but these ghosts only exist long enough to, say, throw at someone on the other side. Why then did Death expect to find the the ghost of the super-sharp scythe hours after it was supposed to be destroyed?
Because everyone is sticking around for longer than they were before, I assume. Maybe Death wasn't thinking too clearly. He was under a lot of stress.
Well, it's not just any object we're talking about.
And don't forget - how long would it take to completely reduce it to ash and slag?
He did state it had to be dead that night, so probably he knew it had to be done quickly. Nonetheless, I don't remember any mention to how much time exactly an object stays in the underworld, it may be much more than an instant.
The ghost of a normal inanimate object may last just long enough to throw it. The ghost of a scythe sharp enough to cut the words out of your mouth, however... Alternatively, because the story says so.
That is the reason death spent so much time on making it sharp. It should be as close to the personification of sharpness as possible to stay in the underworld for a longer time.
Considering how One Man Bucket made use of the ghost of that piece of crockery (hitting another ghost over the head), it's hard to say how long it might've lingered if he'd not broken it in the squabble. The dwarfs certainly believe that funeral weapons' spirits remain intact long enough for their bearers to cross the desert.
Did the Death of humans in also cover Trolls, Dwarves, etc? Or did Dwarves make up their minds faster or what?
He's in charge of everything that dies, except for rats, which he's still sort of in charge of. Everything from the smallest deep-sea worm to... The opposite of a tiny deep-sea worm. In canon, he's been specifically verified to escort to the other realm: humans, dwarfs, trees, turtles, mayflies, golems with souls, music with soul, bogeymen (probably), sea anemone, and deep-sea worms, among others. In Reaper Man, it is likely that the Death of Humans was specifically for humans, and the dwarfs, being vaguely similar physically and mentally but spiritually quite different, likely had something more metaphysical, one of the Darks mentioned in Thud or the sound of a cracking tunnel support.
The question was about the Death of Humans - the evil entity that our friendly Grim Reaper destroyed at the end of Reaper Man. And it would seem that he would have dealt with all the sentient creatures, since his formation explictly took longer because of the complex minds of the sentient creatures.
Humans are probably more numerous than either trolls or dwarfs, and are definitely not as long-lived as either. Humans' beliefs and fears about mortality would naturally predominate, even if all sapient races did share a role in the New Death's manifestation.
Also don't forget the effect of cross-cultural contamination. Sure, it may seem like something silly that those big people who stumble around in the light/somewhat smaller people who go squish when you have a conversation like to talk about and think of. But what if there's something behind it? And death is kind'a scary..
Where does Azrael fit in with all the stuff about belief? No one believes in Azrael on the Disc, aside from Death himself. Yet Azrael is considered the greatest Death, that all the other Deaths came from, in the same way the Death of Rats came from the Death of the Discworld. But that seems to contradict the thing about the personification of Death coming from belief.
He's the Death of Universes. Who knows what universes believe in?
According to The Discworld Companion, Azrael is one of the 8 Old High Ones, the beings older and more powerful than the Gods. To Azrael and his buddies, the Gods are nothing but slightly more annoying versions of human beings. It's also mentioned that they reduced the magic on the Discworld and made humans smaller because of the terrible problems caused by the first Sourcerers. They are not worshipped on the Discworld, with only a handful of Scholars on the Disc able to discover that 8 of these 'entities' exist. They are the observers of the multiverse, and insure that events happen by observing them. So Azrael doesn't exist because the universes believe in him, the universes exist because he and his friends believe in them.
What happened to Sal at the end? She was living on borrowed time from Bill Door/Death, so when his time ran out, did hers as well?
Nobody at the harvest dance seems particularly depressed, so presumably Sal was fine. Miss Flitworth did say that the girl had resumed sleeping normally after the New Death was defeated the first time.