I don't know, I've seen both names used for a similar context. I'm pretty sure that Asura and Shura do have different origins, though the names have a tendency of getting merged in JP translations.
She's actually living in the lord's mansion, not the Dixon house.
The owner of the brothel, and with those words, clearly she met him back when he was active in the capital.
It was hinted earlier on that Noir is probably an isekai character himself, not really a reason so much as maybe a hint at what Noir may do later in the story. From what I've seen throughout this story is that the author may be a bit lacking in the display of relationship advancement, but where...