re: Is Batman a super hero?

Batman is a supergenius. In Tower of Babel, and the variant storylines from it - we see that Batman has a master plan to defeat virtually the entire JLA if he thinks they are stepping out of line. His plan works, making Batman not only a superhero - but possibly the most successful super-villain in the DC verse.

Example: Part of Batman's contingency plans include notes on how to synthesize red kryptonite - a feat Ra's Al Ghul wasn't capable of alone and something which would normally be in the scientific know how of Lex Luthor. And Luthor is? A supergenius.

Also, Final Crisis - who is the guy who really defeats Darkseid? Batman. How? Planning and forethought. Defeating the universe's most powerful bad guy with a single bullet takes slightly above average intelligence. In universe, we have to assume that Batman's intelligence is of such a high level to predict possible situations that he is clearly beyond normal human intelligence.

And... in response that this is not a "superpower", this is well preparedness that borders on precognition. This is not like a boy scout who remember to pack a canteen. Batman accomplishes things that most of the DC verse routinely fails at.

In order to do what he does, Batman has to be intelligent enough to predict numerous potential outcomes, weigh possible strengths and weaknesses of enemies and - as in the case of both Babel and Final Crisis, come up with strategies well in advance to make the outcomes occur. This is why Superman once called Batman "the most dangerous man in the world".

Batman is a superhero, he's just not a metahuman - to use DC jargon. He's just as "powerless" as similar supergenius types like Lex Luthor (or Tony Stark). The key thing here is that while Lex and Stark are known as brilliant inventors, Batman is one of the most brilliant strategists in comic book lore.