Another question is why isn't anyone surprised that Minato is his dad? Did they know since the start of Part 2 or something?
Their Parents
No one knows it's a mystery. Sasuke got his infromation from Orochimaru, Sakura peeped inside the secret filer but others never told how they got to know. I would've wanted to see their face expressions when they got to know.
I dont think they knew in part 1.. But while naruto was awway training with jiraiya (end of naruto) they were probably told by the hokage.
Tsunade probably explained the truth about Kurama and the war before it actually started.