Short answers, pulled from the story.
An anime club is an organization that meets to discuss, show, and promote anime in a local community setting. Members watch anime, read manga, sing karaoke, cosplay, and participate in table top games such as shogi, go, and mahjong. Many clubs also maintain lending libraries and online forums for members.
Anime clubs are increasingly found at universities and high schools. Organizers also use public meeting spaces such as libraries and government centers to reach people outside campus settings.
The core of anime club attendees are in their twenties, but there are generally no age requirements. Adults in their fifties and sixties and teenagers also attend alongside the core membership.
Clubs showing licensed media in a public place must obtain written permission from the domestic rights holder, a process known as Public Performance Rights or exhibition rights. North American licensors including Funimation and Bandai Entertainment have established programs to help facilitate public screenings at anime clubs.
Clubs typically show anime in its original Japanese language track with English subtitles, though fansubs and localized dubs are also used depending on club policy. Screenings are scheduled in blocks with breaks; a twenty-six episode series is often screened over several months. Larger clubs run multiple viewing rooms, one for localized anime and one for fansubs.
Bleach runs for 366 episodes and InuYasha for 167 episodes (191 with InuYasha: The Final Act). At that length, a club may be perpetually screening episodes, which prevents other series from getting a slot. Long-running shows also make it harder for new members to follow a storyline that has already advanced far into its run.