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So like, Ian wanted to take revenge on Michelle's family because he used to be a servant in their family before Michelle was born. (And some things happened) He basically had killing intentions on Michelle. The fact that he isolated him in that castle was so that he could kill him anytime without having any consequences because no one would know that he was the killer—everyone would assume Michelle just died because of the cold.
The reason he accepted the marriage proposal was simply to use the family name of Michelle as they're respected nobles in the south, expanding his authority into the south at the same time. (But you could also argue that he wanted to take Michelle's surname so that he would no longer bear his father's.)

Why is this weirdo pretending to be his own servant for a month? For what purpose? Why a month? None of this makes any seeeeeenssseeeeeeee