Short Answer
Do they not qualify as "derivative works" of intellectual property of
other creators and are they not illegal as such?
Often they are, but not always. Sometimes they are done with the permission of the rights holders, or are sufficiently distinct to not constitute a derivative work, or are trivial enough to constitute fair use (e.g. a Supermanish figure in an editorial cartoon).
But if they were illegal, I think they wouldn't be tolerated so
widespreadely as they are now? Why are such works not being taken
down?
It isn't economically viable to pursue these claims and is bad business to do so most of the time.
Or are they merely tolerated because the copyright owners didn't yet
approach Youtube / Deviantart / Other such sites, asking them to take
them down?
Pretty much.
Indeed, for example, almost every creative author at hosted by the Line Webtoons business actively solicits and periodically displays fan art at the main website and at many social media sites pretty much designed for that purpose, even though Line Webtoons is a for profit business (the name may be just a trade name and indeed probably is as the business is based in South Korea), but either the contracts with the contributing authors or the de facto business practices of the enterprise tolerates this activity and sees it as good for business since it markets the source product. Typically, this is funded with a combination of web based ads, merchandise sold partially at conventions, paid appearances as guests, and rarely but importantly as a motivator, sales in print media or screenplays (e.g. one of their most popular comic strips was made into a live action TV series).
Also - does the so-called Acta 2 (that is, EU Directive on Copyright
in the Digital Single Market), which is already passed, change
anything on this matter? Will it not require hosting websites to
proactively take down such works even before copyright owners approach
them?
As noted in another answer, this hasn't yet been approved and the details are still a controversial work in process. Historically, the E.U. has handled controversy mostly through inaction.
Or am I missing something?
You are missing the practical realities and business model realities of trying to fully enforce derivative copyright rights against infringing works, in a fandom ecology that is structured so that most contributors are ephemeral, working for free for pseudonymous fame and fun, and are anonymous. Often even when works are done by teams of fans, the fans participating don't even know the real names, addresses, or anything else about their colleagues but a username on a website and a web based email address not easily linked to a real person.
Also when work is done by a team of fans, it is arguably making infringing works produced by an unincorporated non-profit association rather than a general partnership, so that the member participants may not have liability for the wrongs of the collective.
Long Answer
To add to the answer by @David Siegel, at a practical level, many owners of intellectual property that gives rise to fan fiction and fan art, even if it would generally be clearly an infringing derivative work, often decline to exercise their legal rights.
Not infrequently, entertainment media authors actually solicit and welcome fan fiction and fan arts so long as it is sent to and distributed by the copyright owner without a profit component other than author funded prizes.
Also, even when these derivative works are not expressly permitted, and the author may even dislike the works being out there, authors often make a tactical/strategic decision that it isn't worth it to litigate the issue.
This is because it can be bad publicity and marketing to crack down on the most loyal and enthusiastic part of your customer base (a special subset of what is known as the Streisand effect), and because litigation is expensive and even if you win against the fans they are often school children with no assets who can pay judgments even if you win. Also, if you sue just one source of infringing fan fiction and fan art, you can end up playing whack a mole and seeing more sites with infringing works pop up as fast as you can shut them down.
Usually what happens instead is that every few years a publisher mounts a coordinated campaign all across its line of entertainment media, all across the Internet and other media, all at once, and writes cease and desist orders and then seeks court injunctions from everyone who doesn't comply, in order to shut down the entire industry with respect to their products for a while. And, since fan fiction and fan art people are usually loyal to the products and well meaning, about 90%-95% of the time, they will comply with cease and desist orders issued in one of these crackdowns without further litigation.
Even if this only produces one or two lawsuits that settle early on, or result in default judgments, however, this is still a quite expensive campaign to wage for the author or the company that owns the rights, because simply identifying the universe of infringers that are out there and finding reliable ways to contact them (all over the world in multiple languages) that meet legal standards for proper notice is a non-trivial non-legal research exercise.
Also, the law firm handling the matter must evaluate on a case by case basis for every potentially infringing derivative work if it is really a derivative work (lots of SEO services put deceptive labels on completely unrelated content to drive clicks and other words are only slightly inspired by the source material and don't really qualify as derivative works at all) and to see if it goes beyond any express permission granted by the author or rights owner, or if it exceeds fair use (or related doctrines such as the scene a faire doctrine that protects works that adhere to the same genre conventions as the allegedly infringed upon work but nothing more).
Realistically, a crackdown like this could cost a rights owner several hundred thousand to a couple of million U.S. dollars or the equivalent to conduct, even if everything goes like clockwork and is a total success, and this crackdowns almost never pay for themselves because the infringers can't be identified in a way that links them to assets from which there can be collection, or have only modest assets that are far less than the costs of the litigation.
FULL DISCLOSURE: I have, over the decades, consumed a fair amount of fan fiction, fan art, and "scanlations" (i.e. scanned copies of works not in English with unauthorized translations of the text), so I've seen this unfold in practice and followed the related legal coverage over the years. I've even been known to attend comic cons, to correspond with fiction and comic authors, and to shop where unlicensed derivative works are being sold by back alley vendors in rural Mexico. This isn't, however, my actual area of practice, because I've never found anyone able to afford to hire me to do it.
