re: the realism of the fight between RF and Batman, it seems that RF was there for a very specific purpose and Batman wasn't it. He beat Batman up because he's a sadist and because Batman kept the fight going, not because it was his goal or necessary for his goal.
Batman probably should have done the old grizzly bear encounter tactic of lying down and playing dead. But that's not Batman.
The question is: What was RF's goal? Did he destroy the letter because it was his goal or as a random act of vandalism? Did he pick up the button because it was his goal or because he was curious once he saw it? Or both?