So... is Itazura na Kiss finished or not?
YES, it is finished.
Why?
The anime finished after the manga:
Anime finished: September 25, 2008
Manga finished: February 13, 1999
MangaUpdates contains information about the anime adaptation and indicates that it is complete.
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
Kotoko, a high school student not known for her intelligence or grace, finds herself living under the same roof as Naoki, the school's brilliant and aloof star, after her house is destroyed.
Kotoko has harbored a long-standing crush on Naoki, a crush he's well aware of and has dismissed in the past.
Now living together, Kotoko sees this as her chance to finally win Naoki's affection, despite his disinterest and the presence of eccentric friends and family members who complicate matters.
The story follows Kotoko as she navigates this unusual living situation and strives to capture the heart of the seemingly unattainable Naoki.