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

My puppy loves tug of war and it's not a problem now and again and it helps with teething. Nipping is normal when they are little too and they don't mean it. It sounds like you are doing everything right. Just keep tug of war to a minimum and encourage fetch games instead. Don't get her neutered until she's had a season either as it can cause behavioural problems. Have fun with her.