Did you actually watch the movie? Sorry, not trying to be condescending but I can't understand people 'not getting it!'
Firstly, not listening to reason? Who's reason exactly? Batman/Bruce has been protecting Gotham for twenty years – fighting to keep all kinds of wackos off the streets - then in a few minutes he wastches a handful of Super-powered aliens destroy a large part of one of America's largest cities, killing thousands (including a lot of Wayne employees)... a city that is only 5miles across the harbour from Gotham. Seems very logical to me that a battle-weary Batman faced with this new threat would want to do something about it... look at the Tower of Babel storyline in th Justice League - he had plans to take down every JL member.
Secondly - the out of control bit... well that also ties in with the previous point, because it is clearly pointed out in the movie that Luthor is manipulating both Batman and Superman into fighting. He really knows which buttons to push on Batman, and I like the fact that in the movie Superman doesn't want to fight. Also have to remember that at this point Bruce sees Superman as a villain, would you moan that Batman was acting out of character if he fought Croc or Clayface like he did Superman...? We all know Bruce is a driven individual to get to where he is, and it has been hinted many times in comic and film that his mental state isn't exactly 'healthy' anyway.
Lastly the nightmare scene – again I liked that... it's part of the subplot that Bruce is having these nightmarish visions of the future, which also shows a rougue Superman (again you wonder why he beats him up later?) - as for Gun Crazy... well yeah he does use a gun there, but did you not notice that it's a future where a Superior and malignant Alien dictator had taken over the Earth... that the survivors were at War, fighting for their very lives against flying Alien soldiers? Sure let's have Batman just punching and kicking people in that situation, just like Captain America did in WW2... oh wait..!
Oh, almost forgot... the Martha moment! Wow, how is this hard for people to comprehend? Bruce dedicated his life to fighting crime because of Thomas and Martha's murder in front of his very eyes... his whole life is a dedicated to their memory. So put yourself in his position... if somebody shouted out your murdered mother's name and said "save her", how would you react? Bruce didn't know Clark's mum was called Martha, and at that moment all that registers was "how does he know my mum's name? Why is he talking about my mum?" ...it's visibly a body-blow, simultaneously makes him realise that Clark is just a man, no matter how super-powered, and also makes him realise that he's gone off the rails, knowing that his mother would be disappointed if she were still alive... it's all there in the comics to be honest, Bruce never get's over the loss of his parents!