Hmm, would be interesting if there would be artifacts during worldgen. Although since the average rate from them is, what, 3 per year, your whole world would end up with hundreds of artifacts before your worldgen even ends. We'll see how that works in the future, eh.
Now lessee.
where do the specifics of what the Artifacts reflects come from, how are they picked?
If the dwarf likes a certain object, like a carpenter likes beds, then they will make one if they get struck by a mood. For dwarves without object preferences, I'm pretty sure it's random what they create. To some degree, I mean stone-/ bone-/ woodcrafters always make a toy, instrument or a craft, but never furniture. Miners like furniture but don't turn into masons as result, gem cutters most often make a perfect gem, at least for me, while gem setters are likely to create a piece of furniture out of a gem. How, hell if I know. Magic, probably.
Who is more likely to get the inspiration, the worker, or the noble?
Only nobles you're able to set yourself, brokers, managers and so on, are able to get into a mood. Sheriff excluded, except if at the time of appointment they're a Recruit and go in a mood. But really, it WOULD be amusing to some degree if a noble would be able to mood as well. Maybe they'd have extra insane moods because they are extra insane compared to normal dwarves.
If i were to change a legendary miner to a woodcutter, would the inspiration reflect the dwarves job, or it's knowledge?
Skill level dictates what job they are of and what mood they follow. So a legendary miner with Skilled Woodcutter would still be a miner and would mood into the closest Mason's shop to make something. Woodcutters would just grab the craftshop to make rock, bone or wood artifact craft.
Why do only some get inspiration in their lives, while some don't?
RNG. And with the rate of 3-4 moods per year, unless you're continually mining, producing etc. to tick the Mood Timer down faster, you're going to have to wait a pretty long time to have everyone having had some mood during their lives. Excluding failed moods due to lack of some item or another.
And finally, if an artifact is forgotten for millennia under a torrent of water or a sea of snow, when/if they're ever found, why do they keep their same worth?
Hmm. At the moment, artifacts don't really do much unless they are a weapon or armor. They're just there to look nice. I wonder how long until they have some special effects like Threetoe's stories say. Anyway.
I figure it's more that the dwarves evaluate the item based on what's it's made of, not what it's purpose is. A goblet made of mica might still be worth 2400 dwarf bucks, even if it can create fireballs out of water and it sings the songs of it's people when everyone is trying to sleep.
As an artifact though, no matter the worth, it's still irreplaceable. Unless some jerk has a mood that produces another, more valuable copy of the object.