So... is Makai Ouji: Devils and Realist finished or not?
NO, it is not finished.
Why?
The anime finished before the manga:
Anime finished: September 23, 2013
Manga finished: February 28, 2018
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
William Twining, a brilliant and proud young nobleman, faces financial ruin after his family's bankruptcy. Driven to find anything of value, he inadvertently summons Dantalion, a powerful demon, from the depths of Hell.
William soon learns that he's caught in the middle of a demonic power struggle. Lucifer, the ruler of Hell, is asleep, and demons vie for the throne. The key to choosing a temporary ruler lies with the "Elector," a human with special authority.
Despite being told he's the descendant of King Solomon and thus the Elector, William, a staunch believer in science, rejects the existence of magic and the supernatural. He's unwilling to accept his role, even as both Heaven and Hell begin to focus their attention on him.