So... is Kaibutsu-kun finished or not?
NO, it is not finished.
Why?
MangaUpdates contains information about the anime adaptation and indicates that it is incomplete.
Watching Order (by release date)
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Synopsis
Kaibutsu-kun is the story of a young prince from a land populated by monsters, appropriately named Kaibutsu Land.
He embarks on a journey to the human world, not for pleasure, but as a crucial part of his training.
This journey is meant to prepare him for his future role as the ruler of Kaibutsu Land: the King.
The anime follows his adventures as he navigates the unfamiliar customs and challenges of the human world, presumably learning valuable lessons along the way that will aid him in his eventual reign.