w h a t ' s . a . d o u j i n s h i ?
According to Wikipedia, Dôjinshi (or Doujinshi) [同人誌] are self-published Japanese or English works, usually manga or novels. They are often the work of amateurs, though some professional artists participate as a way to publish material outside the regular industry. The term dōjinshi is derived from dōjin (同人), literally "same person", used to refer to a person or persons with whom one shares a common goal or interest, and shi (誌), a contraction of zasshi, meaning "magazine". Dōjinshi are part of a wider category of dōjin including but not limited to art collections, anime, hentai and games. Groups of dōjinshi artists refer to themselves as a circle (サークル). A number of such groups actually consist of a single artist: they are sometimes called kojin circles (個人サークル).
In this case Yaoi Doujinshis are a publishing genre which focuses on male/male relationships.
w h a t ' s . a . f a n l i s t i n g ?
It's a list of people who like squeeing at a paticular thing or topic, could be also a character like in this case. The idea is that the bigger the list, the more loved that topic or subject is. Also it's good to meet people who like the same things you do.