Well, on the gay thing...it's really hard to say what guys' feelings are on the subject due to how repressed and frowned upon homosexuality is in our society.
I think "gay" in the context of our society isn't so much about homosexual sex or attraction, it's more about embracing concepts and aspects of the human psychological makeup that's outside of our society's accepted rules. Batman very much represents someone who doesn't bow to social mores, and maintains his stark individuality and psychological honesty despite how it makes him a social pariah.
I think we all have that part of ourselves that, if we're out in the open, or if we didn't curb to some extent, would be frowned upon by society. And most normal people don't have the courage to be themselves dispite that. I mean, if you're a guy, and you like interior design more than football, that doesn't make you gay, but how many guys would have the courage to admit that in a crowded sports bar?
Batman, however, does have the courage to tell everyone and anyone who and what he really is. And he doesn't relent or repent for anyone. I think that's a very big reason why so many people are attracted to him as a character.
This is rubbish. Most people I know would have the courage to say that if they really liked interior design. Most people have varied interests, and most "normal" (and by normal I mean people who are reasonably socialized) are quiet willing to talk about these things despite what people think. Anyone who would is massively insecure about themselves. No one cares what you do or do not like. Nerds often assume such clique-ish behavior exists beyond our younger years, but no, it really disappears. Nerdiness also is often characterized by an inability to see the perspective of others; often they assume another person cares as much about their pet hobby as they do, whether it's hate or affection. Their hyper focus often interferes with their ability to see how complex and complicated other people are, and how they are far less attached to what interests them.
What you're really hitting at here is that superheroes are nerds. There what nerds would like to be. Batman is a horrible person if we were to place him in the real world. First, simply google 'Phoenix Jones' to see how the criminal justice system would view Batman. I won't bring up my detailed essay on everything that makes Batman unfeasible in real life, but most people here already know and say the same things. Socially speaking Batman seems unapologetic, but in fact is massively insecure. He does "lie" about himself. Hence the term "secret" identity. The nerdiest of the nerds definitely often seem to use their hobbies as escapes and defense mechanisms, just like Batman.
Batman is sociopathic, as are most heroes to varying degrees. They go on self-imposed missions, something most normal people do not do. They also think the world, and not them, needs fixing.
Most people are very frank about themselves. In fact, as you kind of said there, most of the time "society" "frowns" upon people because of their frankness. Humans are communicative and social by nature. Batman, on the other hand, is neither. Think about it, in the real world, humans who usually communicate more, and are unafraid to reveal themselves are the successful ones. Politicians and Athletes are all about self promotion and advertising, and ironically much of their **** is public knowledge. It's their ability to act unphased by these things that ultimately make them hard to knock off their pedestal. Batman may seem unphased by popular opinion, but Bruce Wayne isn't. He, like any other hero, seems to need a costume to accomplish what normal people do naturally. Comics usually are all about isolation and solitary people. I think that's largely due to their audience, but probably also the writers. Writing is a very solitary activity as is comic reading. This is not to say that comics only appeal to one group or only represent one thing, but in the basis of many superheroes that theme is definitely present.