So... is Fate/Grand Carnival 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)
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
Fate/Grand Carnival is an anime series that began with a special episode previewed during a New Year's Eve TV special.