Should be I worried or is this normal for my new puppy? 10 points!?

Tug-of-war is not as bad as people think. Tug-of-war will not cause the dog to become aggressive. I think your father is afraid that the dog will think it is dominant if it "wins" too many times. When playing tug-of-war, make sure that you "win" more than the dog does. I'm no expert on dog behavior, but I would say that you are doing everything right. She'll learn not to nip as she gets older.