Yes John Cena's finisher does hurt it hurts your back when he puts you on-top of his shoulders he lifts you up then slams you down to the mat which will hurt your back and maybe cause injury but for some big superstars like big show or Khalil or Mark HENRY and Every other huge superstar will not hurt them that much because of there size.
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It depends. The opponent who, Cena performs the FU actually falls on the mat. However, all wrestlers are trained in a way that they can fall down without actually hurting themselves. So, Cena will hit the move and the opponent will fall down, but wont be hurt much. If the other person, misses the timing, they may get hurt during the fall