Here's something I wonder about: is there only one of each Daedric artifact or are there multiple copies?

Because the Nerevarine got Azura's star and he was Azura's champion, so no reason to give it up, but a few years later the Hero of Kvatch got it with no explanation of how the Nerevarine lost it. Maybe there was more than one?

I especially wonder about this because otherwise it makes the Daedra look very easy to please if they hand out a unique, irreplaceable artifact to some person who did one measly quest for them (and some are really easy, like Nocturnal's quest in Oblivion).

All Daedric artifacts are unique. Each one carries a property where the previous owner loses them after a period of time; sometimes it's a simple misplacement, but mostly the Daedric Prince recalls the item back to their plain of Oblivion and doles it out to another worthy mortal.

They disapear and choose a new owner after some time.http://www.uesp.net/wiki/Lore:Tamrielic_Lore

Artifacts, true artifacts that is, seem to have a mind and will of their own, and rarely stay in the same hands for long. As the player, you are essentially "destined" to receive them, though whether this is due to the hero being doom-driven, or simply the machinations of Daedra, or any number of overlapping surcumstances, is up for debate. It is worth noting that in most cases the Daedric quests to receive these artifacts are not open to any old schmoe who is out wandering in the wilderness. They are only open to the hero. For example, in Nocturnal's quest in Oblivion, it could perhaps be suspected that the quest was merely a ruse, an attempt to put the Skeleton Key in your hands without making it seem like she was just giving it to you. Perhaps in Meridia's quest in Skyrim you didn't simply come across her beacon randomly. Perhaps she purposely plopped it in front of you so that you could clear out her temple.

In conclusion, the Daedra are sneaky gitz.