I like the idea of the party starting in a crappy shack (or just a one person dorm room) with one bed. I think that could be hilarious. Also, excursions into the modern world should definitely happen. "Hi mom, dad. These are my room-mates from school." *Parents stare wide-eyed at the group of obviously inhuman femmboys, begin worrying about what their son is up to. Their worst fears are closer to the truth than they know.*
While the 'Capricious Sidhe' isn't necessarily my favorite trope, I think it actually works pretty well for this, so thumbs up there. I like the idea that the academy was more relevant in the past than it is now. However, I think there should still be *some* kind of greater purpose for it beyond just prestige. Perhaps the Courts are so distant because they are looking outward, either defending the first world from invaders, or invading other worlds. More likely, they recruit the greatest champions into some kind of grand game that spans the cosmos, competing against the other great powers of the multiverse.
At the very least, the First World sounds chaotic and wild enough that there's probably plenty of random monsters and the like, and maybe the occasional incursion from other planes of existence.
In relation to races, tribes, clans and populations and all that, here are my thoughts. Due to the chaotic nature of both the realm and the cultures, perhaps it's difficult for cohesive groups of more than a few hundred individuals to form and hold together. There are a few hundred different races/sub-races in the First World, with some only having a few hundred members, and others having several thousand. However, the more prolific the race, the more fragmented it will be.
Technically, 'tribe' refers to an entire race (or at least sub-race when multiple sub-races exist) however, in practice, it's used to refer to a group that is made up of the entirety of a single race. (barring loners and outcasts of course). Tribes are generally made up of either extremely large and powerful but rare peoples (Minotaurs) or of weaker and inconsequential ones (our Olympians perhaps). So, since the Olympians/aasimars are few in number, and all live in one group (more or less), they would be considered a tribe. Conversely, Minotaurs might be mostly solitary, but they tend not to hold any other allegiances, so if they had to claim one, they would say they were part of the Minotaur tribe.
More prolific races instead organize into multiple clans, usually distinguished by geographic location or extended familial ties. For example, there might be 2000 mountain dwarves in the world, and while they organize into groups, the groups themselves have no broader cohesion. So you might have 'The Gonder Mountain Dwarves' and the 'Black Crag Dwarves' ect. Alternatively, you might have smaller groups that all trace their heritage back to a specific progenitor. So there could be several different herds of 10-20 centaurs that wander around, all of whom share a common legendary ancestor, who might consider themselves a single clan.
Finally, the most powerful and wealthy families, regardless of race, become polities in and of themselves. These groups are actually the most cosmopolitan, since their retainers are drawn from many different races. Many are likely descended from some individual who ascended to one of the Courts, and many families probably pretend to have some allegiance or connection to the Winter or Summer court, though this usually turns out to be more of a detriment than a benefit. (The Noble Fae are more likely to punish a family for being a disgrace than reward them for loyalty)
Also, I like the seed boost. I think that will work pretty well. One question though: how will that interact with ability score increases? Will it still cap at 20, or does the magic of the hero seed break through?
Another thing, when coming up with character background: Since presumably only the best are sent to the academy, we probably all come from pretty pathetic tribes or clans, or there's some other reason why the sad excuses for champions that we are were selected, since with those starting stats we would be beat out by even the most barely above average individual.