user93: Doujinshi are self-published Japanese works such as magazines, novels, and manga. From the description on the Wikipedia page, some of them seem to be akin to visual fan-fiction, though not all.
According to Wikipedia:

Like their mainstream counterparts, dōjinshi are published in a variety of genres and types. However, due to the target audience, certain themes are more prevalent, and there are a few major division points by which the publications can be classified. It can be broadly divided into original works and aniparo—works which parody existing anime and manga franchises.
As in fanfics, a very popular theme to explore is non-canonical pairings of characters in a given show (for dōjinshi based on mainstream publications). Many such publications contain yaoi or yuri (hentai involving two or more males resp. females) motives, either as a part of non-canon pairings, or as a more direct statement of what can be hinted by the main show.

Should questions about these be allowed?

user8134: Yes, question about doujinshi are on-topic for the following reasons:

Some professional mangaka (manga artists) later switch to self-publishing, such as Tachikawa Megumi, who is famous for Kaitou St. Tail and other series published by Kodansha, but is now self-publishing at her website. Due to the fact that publishing print manga is unprofitable and sales have been decreasing in Japan since 1995, Matt Thorn in the Faculty of Manga at Kyoto Seika University predicts that more and more pros will follow this path of switching to self-publishing as time goes on.
Some professional mangaka self-publish doujinshi on the side as a hobby while publishing with a company professionally, such as CLAMP has done. These can include non-official side stories about their own characters (such as if an editor or publisher doesn't want to publish a particular plot idea, so the mangaka draws it outside of the published canon for his/her own gratification), crossovers between their various series, parodies, and doujinshi based on other people's works. A couple examples of mangaka who do doujinshi while publishing licensed series are Sugisaki Yukiru (author of D・N・ANGEL) and Tanemura Arina (author of Kamikaze Kaitou Jeanne).
The number of professional mangaka who got their start in doujinshi would be hard to calculate because there are so many of them.
Manga magazines such as Nakayoshi and Ribon intentionally feature professional mangaka drawing the characters of other professional mangaka. In at least one issue per year, a couple of the mangaka working for that magazine will be assigned to draw a full-color fanart illustration of a character or two from a different mangaka's series that runs in the same magazine. Not only do the readers get a kick out of it, mangaka seem to enjoy the practice. Takeuchi Naoko self-published a Sailor Moon doujinshi artbook that she sold at Comiket, for which she recruited illustrations of her characters drawn by a number of her professional mangaka friends (such as Fujishima Kosuke of Aa! Megami-sama fame, Nekobe Neko who wrote Kingyo Chuuihou!, and Yoshizumi Wataru who wrote Marmalade Boy) as well as illustrations by key animators and seiyuu from the 90s TV anime adaption.
The most famous and largest manga/anime-related convention in the world is Comiket (Comic Market), held twice a year in Tokyo. Unlike the manga magazine matsuri (festival) conventions held in Japan in the summer, and unlike most anime cons held overseas (such as AnimeExpo in California), Comiket is about 90% doujinshika (doujinshi sellers) selling their wares; if you don't care for doujinshi, there is basically zero reason to go to Comiket (other than doujinshi, there is only 1 small-ish dealers' room of licensed titles). Nevertheless, no one in Japan would consider Comiket off-topic for anime/manga. Professional mangaka have been spotted at Comiket purchasing their favorite fanworks. While not technically legal, the Japanese police have never been interested in storming Comiket and shutting down the event. It is acceptable in Japanese culture for doujinshika to make a modest profit off of their works even when those self-publications are derived from fictional worlds/characters created by others.

Doujin works include not only doujinshi comics but also self-published novels (「二次創作小説」, niji sousaku shousetsu which literally means "derivative work novel"), illustrations (「イラスト」, irasuto), hand-painted animation cels (「同人セル画」, doujin seru-ga), and merchandise. Some can be viewed online for free and others are printed and sold.  

user98: Absolutely yes. Many manga authors like Sumomo Yumeka started from doujinshi and then became professionals mangaka. Ignoring these works would mean splitting these authors in two, the professional and the amateur, disallowing questions about part of their career.
Questions about doujinshi are probably more difficult to answer to, because of availability of the doujinshi itself, but an a priori prohibition would be counterproductive.

93: <p>Doujinshi are self-published Japanese works such as magazines, novels, and manga. From the description on the Wikipedia page, some of them seem to be akin to visual fan-fiction, though not all.</p>
<p>According to Wikipedia:</p>
<blockquote>
<p>Like their mainstream counterparts, dōjinshi are published in a variety of genres and types. However, due to the target audience, certain themes are more prevalent, and there are a few major division points by which the publications can be classified. It can be broadly divided into original works and aniparo—works which parody existing anime and manga franchises.</p>
<p>As in fanfics, a very popular theme to explore is non-canonical pairings of characters in a given show (for dōjinshi based on mainstream publications). Many such publications contain yaoi or yuri (hentai involving two or more males resp. females) motives, either as a part of non-canon pairings, or as a more direct statement of what can be hinted by the main show.</p>
</blockquote>
<p>Should questions about these be allowed?</p>
 8134: <p>Yes, question about <em>doujinshi</em> are on-topic for the following reasons:</p>

<ol>
<li><strong>Some professional <em>mangaka</em> (manga artists) later switch to self-publishing</strong>, such as Tachikawa Megumi, who is famous for <em>Kaitou St. Tail</em> and other series published by Kodansha, but is now self-publishing at <a href="http://www6.plala.or.jp/mts/" rel="nofollow noreferrer">her website</a>. Due to the fact that publishing print manga is unprofitable and sales have been decreasing in Japan since 1995, <a href="http://www.kyoto-seika.ac.jp/eng/edu/manga/" rel="nofollow noreferrer">Matt Thorn</a> in the Faculty of Manga at Kyoto Seika University <a href="http://matt-thorn.com/shoujo_manga/colloque/index.php" rel="nofollow noreferrer">predicts</a> that more and more pros will follow this path of switching to self-publishing as time goes on.</li>
<li>Some <strong>professional <em>mangaka</em> self-publish <em>doujinshi</em> on the side as a hobby <em>while</em> publishing with a company</strong> professionally, such as <a href="http://www.doujinshi.org/browse/author/29585/CLAMP/" rel="nofollow noreferrer">CLAMP</a> has done. These can include <strong>non-official side stories</strong> about their own characters (such as if an editor or publisher doesn't want to publish a particular plot idea, so the <em>mangaka</em> draws it outside of the published canon for his/her own gratification), <strong>crossovers</strong> between their various series, <strong>parodies</strong>, and <strong><em>doujinshi</em> based on other people's works</strong>. A couple examples of mangaka who do doujinshi while publishing licensed series are <a href="http://www.doujinshi.org/index.php?P=LIST&amp;T=author&amp;ID=14141&amp;S=7" rel="nofollow noreferrer">Sugisaki Yukiru</a> (author of <em>D・N・ANGEL</em>) and <a href="http://www.doujinshi.org/browse/author/13684/Tanemura-Arina/" rel="nofollow noreferrer">Tanemura Arina</a> (author of <em>Kamikaze Kaitou Jeanne</em>).</li>
<li>The number of professional <strong><em>mangaka</em> who got their start in <em>doujinshi</em></strong> would be hard to calculate because there are so many of them.</li>
<li><p>Manga magazines such as <em>Nakayoshi</em> and <em>Ribon</em> intentionally feature professional <em>mangaka</em> drawing the characters of other professional <em>mangaka</em>. In at least one issue per year, a couple of the <em>mangaka</em> working for that magazine will be <strong>assigned to draw a full-color fanart illustration of a character or two from a different mangaka's series that runs in the same magazine</strong>. Not only do the readers get a kick out of it, <em>mangaka</em> seem to enjoy the practice. <a href="http://mangastyle.net/sailormoon-artbook-vol-infinity/" rel="nofollow noreferrer">Takeuchi Naoko self-published a <em>Sailor Moon doujinshi</em> artbook</a> that she sold at Comiket, for which she recruited illustrations of her characters drawn by a number of her professional <em>mangaka</em> friends (such as Fujishima Kosuke of <em>Aa! Megami-sama</em> fame, Nekobe Neko who wrote <em>Kingyo Chuuihou!</em>, and Yoshizumi Wataru who wrote <em>Marmalade Boy</em>) as well as illustrations by key animators and <em>seiyuu</em> from the 90s TV anime adaption.</p></li>
<li><p>The most famous and largest manga/anime-related <a href="https://anime.stackexchange.com/questions/tagged/conventions">convention</a> in the world is Comiket (Comic Market), held twice a year in Tokyo. Unlike the manga magazine <em>matsuri</em> (festival) conventions held in Japan in the summer, and unlike most anime cons held overseas (such as AnimeExpo in California), <a href="https://anime.stackexchange.com/a/22858/8134">Comiket is about 90% <em>doujinshika</em></a> (<em>doujinshi</em> sellers) selling their wares; if you don't care for <em>doujinshi</em>, there is basically zero reason to go to Comiket (other than <em>doujinshi</em>, there is only 1 small-ish dealers' room of licensed titles). Nevertheless, no one in Japan would consider Comiket off-topic for anime/manga. <strong>Professional <em>mangaka</em> have been spotted at Comiket</strong> purchasing their favorite fanworks. While not technically legal, the Japanese police have never been interested in storming Comiket and shutting down the event. It is acceptable in Japanese culture for <em>doujinshika</em> to make a modest profit off of their works even when those self-publications are derived from fictional worlds/characters created by others.</p></li>
</ol>

<p><em>Doujin</em> works include not only <em>doujinshi</em> comics but also self-published novels (「二次創作小説」, <em>niji sousaku shousetsu</em> which literally means "derivative work novel"), illustrations (「イラスト」, <em>irasuto</em>), hand-painted animation cels (「同人セル画」, <em>doujin seru-ga</em>), and merchandise. Some can be viewed online for free and others are printed and sold.  </p>
 98: <p>Absolutely yes. Many manga authors like <a href="http://en.wikipedia.org/wiki/Sumomo_Yumeka" rel="nofollow">Sumomo Yumeka</a> started from doujinshi and then became professionals mangaka. Ignoring these works would mean splitting these authors in two, the professional and the amateur, disallowing questions about part of their career.</p>

<p>Questions about doujinshi are probably more difficult to answer to, because of availability of the doujinshi itself, but an a priori prohibition would be counterproductive.</p>
