"There are multiple fae races. Do all of them trace their lineage back to Oberon, Titania, and Maeve? Is there a record of when each separate race came into being, and when was the last time that happened?"
"How do you decide which mythical beings are real in Toby's world? Along with kitsune, are oni, kappa and tengu real? How about jiang shi? What about Abalone Woman from the mythology of northern California? When the fae came from Europe, did they displace or remove natives, or was there no one in California? (I remember talk about settling briefly in the book, but I cannot recall the particulars)."
First, the out-universe answer. All fae in Toby's world trace their lineage back to some combination of Oberon, Maeve, and Titania. Some have two of the First in their background, some only have one. The Cait Sidhe have all three, but they're a special case (as they so often are). This means that only mythical creatures whose backgrounds are somehow malleable can be subsumed into Toby's world. Kitsune, Tengu, Bakemono, Tsukumogami, Shi-Shu, Menehune, Nawao, and other creatures who don't have a very firm "and then so-and-so begat..." or who were originally presented as a lone individual and can be made into a race (such as the Blodynbryd) exist in Toby's reality. Other creatures, such as most of those found in Australian mythology, and pretty much all of Inuit or Native American folklore, don't exist, because there's no respectful way to say "and Oberon was your daddy's daddy's daddy, yay!" It's a juggling act. If I were establishing the rules of this universe today, I would probably either keep it more Euro-centric, to avoid possibly disrespecting another culture's folklore, or find a way to incorporate other fae monarchs in other places. I didn't do that when I wrote the first book, and so these are the rules I have to work with. If they're not descended from the Three, they don't exist.
Oh, and jiang shi don't exist because they're very explicitly dead in every accounting I can find. They'll eventually show up in InCryptid, which has very different rules.
Now, the in-universe answer:
We've established that all fae races trace their lineage back to the Three, by way of their Firstborn, who are the immediate descendants (children, although not always in a recognizeable sense) of the Three. The Undine, for example, were wept, not born, but are still children of Maeve. This includes Faerie's various monsters, although, so far as anyone knows, all the monsters are the result of the Firstborn tinkering, not the Three themselves. (This may or may not be true. I haven't decided, and since it's one of my few bits of beautiful indecision, I'm holding it for a while.) Regardless, everything in Faerie finds its way back to the Three, one way or another.
Here's where it gets complicated. The children of the Three are Firstborn, and while they can be similar, they are always entirely unique in all the world. Most of them can blend into their own descendant races, pretending to be what they create, but they'll always stand a little bit apart, no matter how hard they try to disappear. They get good with illusions and minor shapeshifts, because otherwise, they'd never have any peace. No one knows how many Firstborn are still alive. They don't want anyone to know.
The libraries track the lineages and the origin points, when they're known. Good luck getting a pass to the stacks.
Any time a Firstborn takes a new lover and has children, the child or children will begin a new race. Firstborn are more fertile than normal fae, partially because otherwise, no races would ever become established. The Roane Firstborn, for example, had three children, and those three went on to beget all the rest of the Roane. As for when the last time this happened was...
Firstborn still exist. Firstborn may still have children. So maybe it was yesterday. But things move slowly in Faerie, and children are only born so fast. So who knows?