So... is Sakura-sou no Pet na Kanojo finished or not?
NO, it is not finished.
Why?
The anime finished before the manga:
Anime finished: March 26, 2013
Manga finished: May 30, 2015
MangaUpdates contains information about the anime adaptation and indicates that it is incomplete.
Watching Order (by release date)
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Synopsis
Sakura-sou no Pet na Kanojo tells the story of Sorata Kanda, a seemingly ordinary high school student who gets stuck living in the Sakura-sou dormitory, a place known for its eccentric residents.
He initially wants to escape the dorm, but his plans change when Mashiro Shiina, a beautiful but socially awkward art prodigy, arrives and needs his help.
Surrounded by talented and unique individuals, Sorata begins to question his own abilities and strives to find his own special skill.
The anime explores the themes of friendship, love, ambition, and self-discovery as Sorata navigates life with the other residents of Sakura-sou, learning and growing alongside them.