So... is Abashiri Ikka finished or not?
NO, it is not finished.
Why?
The anime finished after the manga:
Anime finished: November 21, 1991
Manga finished: January 01, 1973
... But MangaUpdates contains information about the anime adaptation and indicates that it is incomplete.
Watching Order (by release date)
Here you have all the anime relations we detected ordered by release date, so you can see the reason for this status in context and also use it as watching order.
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Synopsis
The Abashiri family, a notorious crime syndicate, decides to pull off one last heist. The patriarch, Daemon Abashiri, reveals a secret: his youngest child, Kikunosuke, is a daughter, breaking a long line of male heirs. Determined to give her a normal life, he enrolls her in the prestigious Paradise Academy.
However, Paradise Academy is far from a haven. Instead of a refined education, Kikunosuke finds herself in a cutthroat environment where survival is a daily struggle. The school is full of eccentric teachers that want nothing more than to see their students fail and even potentially die.
Now, Kikunosuke must navigate the treacherous halls of Paradise Academy, facing deadly challenges and bizarre situations, while trying to escape the shadow of her family's criminal past. Her goal is simple: to survive the academy and find her own path, all while trying to outwit the deadly instructors.