Why does Mint have rabbit ears? In Galaxy Angel, it seems Mint and her family all have these droopy rabbit ears above their real ears. 



I know that she likes cosplay so are these fake? In all of the anime seasons I don't see her without the rabbit ears and she seems to be able to move them as if they're real. I've read that the BROCCOLI game has some insight into the ears but I've never seen the game or could find any info about it.
It is unknown officially whether they're real or fake. As you mentioned, Mint's father, Darno, has these ears as well:



The reasons why Darno has these do not appear to be stated, nor are they very elaborate for Mint. It is believed that they are fake due to her losing them later in the series. From the Galaxy Angel Wiki:


  She is notable for having a pair of rabbit ears above her human ears, a trait shared by her entire family and the family pet. They can move depending on her emotions and can flap rapidly for flight. Although generally considered real, they were shown to most likely be fake in the third season, after an ordeal with a duck helmet completely removed her hair and rabbit ears, while leaving her real ears attached.


So, while they are considered to be fake for the reason stated above, it has never been officially revealed one way or another.