So... is Oruchuban Ebichu finished or not?
NO, it is not finished.
Why?
The anime finished before the manga:
Anime finished: October 01, 1999
Manga finished: January 01, 2008
MangaUpdates contains information about the anime adaptation and indicates that it is incomplete.
Watching Order (by release date)
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Synopsis
Oruchuban Ebichu centers around a hamster named Ebichu who dedicates herself to serving her owner, referred to as "Office Lady."
Ebichu enthusiastically takes on all sorts of household chores and tasks, striving to make OL happy.
However, Ebichu's efforts often lead to comedic mishaps, especially due to her love of ice cream and OL's complicated relationship with her boyfriend.
These mishaps frequently result in Ebichu being punished, but she remains undeterred in her mission to bring joy to her beloved master, even if it's just a little.