So... is Uchuujin Tanaka Tarou finished or not?
NO, it is not finished.
Why?
The anime finished before the manga:
Anime finished: March 26, 2001
Manga finished: September 01, 2004
MangaUpdates contains information about the anime adaptation and indicates that it is incomplete.
Watching Order (by release date)
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Synopsis
Uchuujin Tanaka Tarou tells the story of Takashi, a typical fifth-grade boy whose life is turned upside down by the arrival of a bizarre transfer student named Tarou Tanaka.
Tarou is clearly not from around here – he's blue, has glowing eyes, and a single horn. Takashi becomes obsessed with uncovering the truth about Tarou's origins.
Driven by his curiosity, Takashi tries to follow Tarou and observe his behavior, but he often finds himself caught in Tarou's wacky and otherworldly pranks.
The anime focuses on Takashi's attempts to understand Tarou and the humorous situations that arise from their interactions.