Responses
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Answer to the first question is yes, nina is the reincarnation of the first king's lover. As for the 2nd one, as far as i can remember, it was the pope who suggested to kill the other saintess(nina) and even though beato and nina bonded, his sin was that even though he knew of the plan of killing her, he didn't do or say anything to stop them from killing her.

Contains spoiler i guess but question here
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I read in the comments before that Nina is also a saintess and she was imprisoned because there can only be one.
Is she also the reincarnation of the first king's lover thats why he feels longing??
As for beato, he's the one who suggested to lill the other saintess right?? I wonder why is that nina's memories seems like beato cares for her...