OP, I don't know what you're smoking but you're so far from speaking sense you dragged me out of hiatus to rebut your total fucking nonsense.
And yes I am cursing. Because I don't care for JKR and her TERFism but you are so far wrong on some of these that I am feeling forced to explain her damned canon and defend it because if you're going to hate and pick at JKR you should do it for the shit she's actually done and not for made up nonsense.
Lets dig into this, right?
I think by far the strangest thing about HP Veela is the fact that they're so associated with the French witches and wizards despite being based on a Slavic myth.
This is primarily due to the existence of Fleur, who is part-Veela, not fully Veela. Veela themselves in canon are more directly associated with Bulgaria, which is a little ways off (South Slav as opposed to the regions more likely to have Vila stories), but we first see them as the Bulgarian Quidditch mascots. That is at least closer regionally and culturally, and given JKR's fuck up on the accents there, there's at least a logical throughline to the location.
Like ... the vila are a species of Slavic fae and/or nymphe-like creatures. Like, the Basiliskos, the elves, the boggarts and the vila are all so far removed from what they were in their original myths. Basiliskos and vila aren't even spelt correctly, and what she did with boggarts and elves is honestly wild.
I'm SO GLAD you recognise Vila as some kind of fae! This is going to make some of the later explanations much easier, because you seem to have drastically narrowed your definitions in a way that is absolutely stupid when it comes to dealing with something as broad and thematic as folklore.
And honestly... no, some of these are not far at all from their original inspiration.
The Basiliskos was a North African bird with a serpent tail whose touch is deadly and venomous breath would slowly wither you away. It could kill ANYTHING.
I do not have the least idea where you got the idea that the Basilisk is a bird from. It... honestly sounds like you've gone and mixed it up with one of the dragon versions from the old Ology books? Maybe the amphitere? (Which is a kind of dragon, like a feathered Jaculus from old Bestiaries, bc old Bestiaries are wild).
To be clear, Basiliskos is from the Greek, From Basilieus meaning "king" - hence it's title as king of serpents. It has always been a serpent or reptile, usually with a crest which resembles a crown.
Now, historically "serpent" was a very broad term that could also refer to lizards, wyrms, reptiles of various kinds - this is why some dragons are also called serpents, and why the serpent in the book of Genesis was still a serpent when it had legs and why Basilisks could be serpentine or reptiles. Medieval bestiaries are wild. But... this means that at most the Basilisk was like an actual IRL common basilisk (Basiliscus basiliscus) aka the Jesus Lizard - a lizard with four legs and some kind of head crest - and was just as likely to be a serpent - has been depicted as a serpent!
The more birdlike versions of the Basilisk are generally more associated with the Cockatrice - which is also mentioned (albeit fleetingly!) in canon - but Basilisks being able to kill with their gaze and being some form of toxic is recurring, and the idea of being able to turn back their gaze with a mirror is taken (as many things in HP are) from the classics, from the myth of Perseus and Medusa. JKR liked the classics.
So this? You were all wrong. Moving on.
Elves are from the Germanic Alf, referring to the magical creatures of either light (ljosalfar) or dark (dokkalfar) that were ambivalent towards humans.
Mmm... Ambivalent is a bit light, and also you're missing a variety - the Svartalfar! Which makes sense, because the "Swarthy elves" are a confusing one even to modern scholars of Norse myth (note: Norse, not Germanic, Alfar are Scandinavian) who debate if they're a third type of Alfar or just dwarves. Hell, even the Dokkalfar are sometimes conflated with dwarves.
This is why you shouldn't allow Christians to destroy all records of prior faiths. Makes study a lot harder.
There's also sometimes the alv which are like... little Scandinavian sprites because! This is the thing I'm shocked you don't recognise if you're able to recognise Vila as being something like fae, the alfar are kind of fae-adjacent as well. In Scandinavian folklore there's a BUNCH of fae-like creatures from the ra place-spirits to the alfar to the household tomte and tonttu (though that last is Finnish really) to Trolls! Yes, trolls. Because you get in Scandinavia stories of Troll-cats and Troll-rabbits and this is because Trolls fill a similar niche to fae in the broad folklore. It is a broad category and alfar can fit into it, and can/do overlap with trolls. Alfar and Trolls can steal people away, including children. Thus, elves and fae are conflated and have been for quite a long time, which one can argue was exacerbated by Tolkein using the Ljosalfar as his inspiration for elves but also isn't that surprising because "fairies" in England has a very different connotation to "fairy" - and it's also why "elves" to mean the upright, full-size, humanlike fae has come into common parlance.
As for the association with House-Elves... Brownies? Hobs? Fenodyree, silkies , bwbach? Hell, tomte and tonttu and domovoi and dvorovoi and kikimora. There are so many household fae throughout Europe, because it was common practice to put down milk for the fairies, especially household fae. JKR's decision to conflate them and name them "House Elves" was both a broad simplification of a recurring part of European folklore, and part of a (clumsy and later dropped) slavery metaphor. You can see how they start in the household fae folklore - it is not a hard thing to consider as to how they became enslaved house elves.
Elf as a broad term for fae
European Household fairies combined
Call them House Elves because fairies has a different connotation.
This is uh... not complicated. I figured that one out when I was about twelve.
Boggarts were a type of Unseelie Fae that either served as household mischief, stealing your cutlery and trinkets, or as horrifying swamp monsters, stealing children.
Boggarts, Bogles, Bogies, Bugges, Bugbears, BOGEYMEN - it's... again, its not complicated, this isn't some kind of Unseelie Fae, its just the bloody bogeyman. Unseelie is a very modern application to distinguish malicious fae from non malicious (and I can't help but wonder if I served to add to that, with my use of it here on this blog, but just as likely it's one of any of a dozen popularly published books).
Now, as has been pointed out by @thecreaturecodex, what JKR described with the Boggart is actually closer to a Brollachan (CC's; Here; Second Paragraph here). OP, you're being far too narrow in your folkloric definitions because the thing is shit changes? Folklore shifts? Things syncretise? The Boggart is a malicious, at times shapeshifting fairy creature and there are so many names because as with the folkloric Black Dog there are as many types as there are names as there are places, and as JKR simplified Black Dogs with the Grim (you know Padfoot is another name for Black Dogs? Shuck? Cu sith? Barghest, Yeth Hound, Shug-monkey, I could go on) she simplified the Boggart too so she didn't have to use a myriad words for what boiled down to very similar beasts across the few mentions they had in her books.
It is a matter of narrative efficiency.
Vila were a type of Slavic shapeshifter, who might be found dancing in circles naked to lure in men, however joining uninvited meant death, and would turn into hurricanes or wild animals like deer but have ZERO bird or fire association.
Uh.... Vila or Wilis are the variously, fairy nymphs related to fae, or in popular culture:
The wilis appear in Adolphe Adam's Romantic ballet Giselle, first danced in Paris in 1841, as the ghosts of young girls who were betrayed by their lovers and who died before their wedding days.
Spirits of women who died or were drowned either due to heartbreak or by a shitty lover.
There's also some overlap with the Samodiva also called the Samovila (note that similar ending) which can sometimes have a fire association. The Veela are definitely the most divergent from their original mythology but, they're also drawing from a multitude of sources. Ones I could figure were:
Swan Maidens for the bird aspects
Harpies for the monstrous aspect
Other seductive and/or shape-shifting fae throughout Europe such as the French Korrigan women, Asturian Xana, Galician and Portuguese Enchanted Moura, and Irish Leannan Sidhe for the supernatural allure.
Possibly a commentary on Slavic Mail Order Brides and trafficking (see their status as mascots).
Possibly a commentary on "Hell hath no fury like a woman scorned" by giving these beautiful creatures means to retaliate.
JKR's own bad case of Not Like Other Girls.
Yes, they're deeply divergent. Yes almost none of these inspirations is actually meaningfully touched on. But they are also there! Folklore is much broader than you seem inclined to think on or realise (or... research, frankly. Basiliskos being a bird).
And, as you admit yourself:
Like, after a certain point of making your own mythology for those creatures you've just got to admit they're no longer any close to what the inspiration was, and therefore, should simply be named something else.
She did name the Veela something else, and given Samodiva as an influence can also be called Samovila sticking to the Veela sound makes sense, (especially as Wilis was taken by theatre). She also renamed House Elves, but that just seemed to hack you off because they're not elves - elf is a broad term. Fae is a broad term. Folkloric categories are notably vague, if you want a good explanation of it, honestly go and watch OSP's video on dragons.
She really tried with Veela but girl, it's not that hard to figure out what they were supposed to be based on. And why are they all French??
They're not! Even in canon, they're not! The Veela we know of in canon are 1. Bulgarian mascots and 2. Fleur's grandmother.
Fleur's grandmother may not even be French! Fleur is notably and specifically part-Veela, for all JKR's later "all Veela are women" it's clear you can also get part-Veela, so presumably either:
JKR's a dipshit and there are male Veela (which would go against the myth but be biologically plausible (but as I've examined elsewhere would also violate her TERFery so odds are she won't do that even though it'd be more interesting)), OR:
Veela can reproduce through parthenogenesis to create genetically limited but pure veela not unlike Komodo Dragons or the lesbian lizards, or with humans to produce part-veela.
Fleur herself is not a Veela. Her sister Gabrielle is not a Veela. Her mother Apolline is not a Veela. The idea that they're full-Veela is fanon created to try to square the folklore and JKR's statements with the supposed "part-Veela", and has no bearing on canon which describes them as part-Veela.
The Veela are not French. Some Veela may be French, because the Veela of HP are not a regionally-locked piece of folklore but, within the story actual people who may, shock of all shocks, want to emigrate.
The vila to Veela transition confuses me the most. Even her boggart confuses me less.
This is probably a YMMV thing. But I hope the explanations here help.
The point is: you change things in a story to serve the story. If you diverge from the mythology you explain it or you create a variant name to distinguish it. But also, plenty of media don't do that. Is anyone gonna go after Supernatural or Grimm or... or Teen Wolf? for making every single monster of the week a human in some face make up? Is anyone gonna discuss some of their batshit mythologies? No, because those are pulp TV. HP is kids boarding school fantasy, it's own kind of YA fantasy pulp, it's just also massive and increasingly being picked over by adults who hate it for JKR's sins.
HP has it's own sins (HIV-Lycanthropy analogy; Fatphobia and Ableism, JKR's terrible approach to Native American mythology; the Jesus metaphor of Harry, the background misogyny and Not Like Other Girls-ing; fucking Nagini) but if you're going to get mad at it get mad for what's actually there and not things you've evidently made up in your own mind (Basiliskos being A BIRD???).