So... is MÄR finished or not?
NO, it is not finished.
Why?
The anime finished before the manga:
Anime finished: March 25, 2007
Manga finished: June 13, 2007
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
Ginta, a boy obsessed with dreams of a magical world, finds his wish granted when a mysterious door transports him to MAR Heaven.
This world is filled with powerful, weapon-like items called ARMS.
While initially thrilled, Ginta discovers that MAR Heaven has a dark past of war and faces the threat of another conflict.
He must now navigate this dangerous new reality.