Alicornutopia

... Oh that's interesting. Is it possible to vassalize someone's daemon, but not them?

... Oh geez. Fairyland was creepy enough without the potential of someone literally stealing your soul.

Yeah, I think if some fairy had a daemon's name that would work that way.

Yikes. If I’d considered it, which I hadn’t, I’d have thought that getting one would mean getting both. Effectively it would because they know each other’s names, but still…

In canon MCU, as best as I can tell, Tony chose the name JARVIS based on Howard’s butler’s name (Edwin Jarvis), and then backronymed it to Just A Rather Very Intelligent System at some point during the creation of JARVIS, probably before sentience. This does not match Lake of Sky, so probably will not come up in Effulgence unless it’s decided that this is true for Yggdrasil. However, given this naming, would a fairy be able to vassalize him with the name “JARVIS” but not the words? On the one hand, that’s sort of like initials, which don’t count; on the other, JARVIS is still more namelike than Just A Rather Very Intelligent System, so JARVIS might still be the name with Just A Rather Very Intelligent System being the etymology.

JARVIS's name is Jarvis, in this instance. The backronym came second.

How common one-of-kinds are? A few per continent? Less?

Less. We've only described three; there might be a few more but the total number is small, probably single-digit.

Are there an infinite number of fairies to go with this infinite land area? If not, about how many are there? I'm getting the impression that the Queen's influence is felt at least ten continents away from the main court in every direction, and that there are fairies farther away who rarely if ever have cause to notice she exists, so that's at least 400 continents' worth of fairies, and I expect that's an underestimate.

The Queen's influence is not felt literally everywhere. New fairies typically appear on continents/in areas with a low but nonzero existing population density of fairies. (Breeders obviously follow their own rules, but when their courts get bigger they get harder to manage and are likely to splinter and have bits of them move away.) There are fairies too far away to have heard of the Queen yet, but not most of them and not an infinite number.

Here is a Fermi estimate for total number of fairies which I am in no way committing to being within several orders of magnitude of accurate: 10 billion.

Well, 10 billion and 400 continents’ worth certainly aren’t within several orders of magnitude of each other. I’ll assume yours is closer to correct unless a better number comes along, though.

It’s implied that the first of any breeder fairy kind usually just starts, like starter kinds do. Do they have childhood phases like others of their kind, or do they start knowing various things like other starting fairies? If the latter, does that include how their specific kind generates children (since it is often different from the way other kinds or mortals generate new children)?

I'm not sure how many fairies you're imagining there are per continent. It's not that many. I handwaved a vague semblance of a court size power law with 500 being the ceiling.

Foundational breeder fairies have childhoods (and often get caught by nearby other fairies during them). They do get an instinctual boost towards figuring out how to reproduce.