So... is Detroit Metal City finished or not?
NO, it is not finished.
Why?
The anime finished before the manga:
Anime finished: October 28, 2008
Manga finished: April 23, 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
Detroit Metal City is a comedy about Souichi Negishi, a mild-mannered college graduate with a love for sweet pop music.
However, to pay the bills, he fronts a wildly popular death metal band called Detroit Metal City, adopting the persona of the demonic Johannes Krauser II.
The anime follows Negishi's struggles to reconcile his true self with his shocking stage persona and manage the absurd situations that arise from his band's over-the-top performances and dedicated fanbase.
He tries to maintain some semblance of a normal life, pursuing his preferred music and navigating a potential romance, all while desperately trying to keep his two worlds from colliding in disastrously funny ways.