Orinoko's feed

So they are saying that the FL and her brother look alike, but she can't be the duke's daughter cause she doesn't have silver hair, by that logic the brother also isn't his child cause he as well doesn't have silver hair (i know that the members of the family can contract spirits, but if he wasn't capable of doing it would they be saying the same thing to him), and am i the only one remembering things wrong but didn't she have contact with an ice spirit when she was in the cave what happened with that ?