I just read this and I have a lot of questions. It's like random infos are just thrown her...

I think mixed in this case just means not full red eyes. This also means you don't get all the super powers associated with the family.
Duke are usually closely related to the royal family. Duchys are usually awarded to 2nd or 3rd princes who won't become king. So just the fact that someone is a Duke or Duchess, one can assume they are somehow related to royalty.

Thank you (⌒▽⌒)