So... is Hana yori Dango finished or not?
NO, it is not finished.
Why?
The anime finished before the manga:
Anime finished: August 31, 1997
Manga finished: December 22, 2019
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
Makino Tsukushi, a working-class girl, enrolls in the prestigious Eitoku Academy hoping for a peaceful high school life.
However, her desire for anonymity is shattered when she defends a friend against the F4, a group of four influential and wealthy boys who rule the school.
This act puts her directly in their crosshairs, making her a target of their relentless bullying.
Despite the challenges, Makino refuses to be intimidated and begins to navigate the complexities of the school's social hierarchy, while also developing feelings for one of the F4, Rui.
She discovers that appearances can be deceiving and learns there's more to these seemingly untouchable boys than she initially thought.