I very much enjoy our discourse, I find it incredibly fun to think through the steps of world building--and it is only made easier by the criticism/comments/input of others! This thread is both repository for myself and center for discussion about the contents therein.
Well... Fate could be studied in a sense. The Gods, who are the original users of Fate magic, had little interest in the subtly and nuance of what is possible with this power as they basically used it to try give themselves temporary advantages over the other Gods in a bid for supremacy (with the hope that once they "won", they could weather the inevitable storm--of course, no one was willing to risk ENOUGH to grant them a total victory in the first place [kind of like Warhammer Chaos Gods]). Later on, it is the Elves who use Fate to separate the mortal world from the Gods, it wasn't really used by most, but the King of the Elves was a Fate user (more masterful than the Gods), and his legacy not only survived the (later) destruction of the Elves (and himself), but also continues to survive on today in the form of certain powerful figures. The point is, there are people who have complex ambitions and modi operandi who have a specific knowledge of how Fate works, what it is capable of (in both an obvious and obscure sense of using Fate), and have definitely had the chance to pass it down in a learned way. So in that sense, it could be a "school".
For the average person? Well, it is probably more chance that Fate magic is triggered by accident than on purpose--and they probably aren't aware that they are using it at all. It's rare for a random person, especially a non-human to be able to use Fate magic without being somehow taught about it, but anything can happen, right? For humans, Fate can be used normally--i.e. bargain for something now and receive an opposite reaction later--but like I said it is also an integral part of their beings. All life is cursed in some form. Most beings "suffer" from the separation of thought. A good portion of beings are also mortal, doomed to blossom, wither, and be reborn. But only Man is cursed with the magic of Fate--which basically means they inevitably get stronger in their prime and decline in wisdom or ability with age (like real life, not all humans age the same way, or at the same time of course. Some being quite useful into their latter years, with others being confined to mediocrity or misfortune from young age.)
But also remember that Fate is no certain thing. A human can fail/be killed/die/fall in their prime, and this disruption of a (somewhat) stable use of Fate will send ripples through others' destinies. If a particularly fateful human is killed in a duel (by some crazy bad ass), it is possible their child could inherit the fatefulness lost (even multiplied, as losing what is a certain victory is a big swing), or more cruelly, the killer of the human could inherit their fatefulness. I think it's random for now.
*Crazy shit can happen like passing your bad/negative fate off to other people and just keep going on normally. Dwarves also make little use of Fate/are not even really aware of it. This makes them difficult to defeat, though their successes are often more moderate, and they are prone to suffering. They can however inherit Fate like any living being.
As far as a story about the use of Fate itself... I think that the downfall of Iyomuij (the aforementioned Elf-King) is probably a good place to start, which also happens to be part of the larger epic (which is more a history than an account). So perhaps I will expand upon it?