So... is Kappa no Kaikata finished or not?
NO, it is not finished.
Why?
The anime finished before the manga:
Anime finished: April 04, 2005
Manga finished: July 15, 2010
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
A man impulsively buys a kappa, a mythical Japanese water creature, from a pet shop.
He names the kappa Kaatan and attempts to raise him using a guidebook.
However, training Kaatan proves to be much more difficult than expected, as the kappa is often forgetful and uncooperative.
Despite the challenges, the man patiently persists in his efforts to nurture Kaatan and make him a well-behaved pet.