Why Naruto's hand was not injured using rasenhurikan
It's explained here: 


  Naruto is able to overcome these flaws by learning Senjutsu. By coating the Rasenshuriken in Senjutsu chakra, its shape is maintained after formation, meaning that he can use it as a projectile and, as a result, that he no longer needs to worry about damaging himself. 


I'm not sure if this was explained in the anime since I only read the manga so if it's not, I suggest reading the manga starting at Chapter 400, which I believe is the start of Naruto's training for Senjutsu.