...if Green Lantern rings are so powerful it can scan entire sectors why didn't Abin Sur's ring scan lead the ring to BATMAN rather than Hal Jordan? Are you saying that Hal is more fearless than Bruce?
Easily. Bruce Wayne's entire life is shaped by fear. Everything he does is to master the feelings of fear and helplessness that his childhood trauma induced in him. He's harnessed that fear and turned it outward, used it as a weapon against criminals. But he couldn't understand and use fear as effectively as he does if he didn't feel it.
...why do people continue to live in Gotham knowing the city is nothing but a cesspool of the most dangerous criminals (Joker, Freeze) etc?
Well, the rents are probably quite low. Also, Gotham's a center of art and culture. Nowhere else have the art forms of giant novelty props and robotic replicas of extinct predators achieved such heights.
And to that effect, why isn't Metropolis a ghost town considering it gets attacked by unstoppable aliens, semi-robotic aliens, giant robotic aliens, and every other supervillain trying to take out Supes?
I'm not sure about the comics, but in S:TAS, it was stated that LexCorp built most of Metropolis and employed most of its citizens. Maybe their jobs required them to stay.
Besides, yeah, the comics focus on those times when someone or something goes after Superman, but that's only a dozen times a year -- actually more like two or three times a year, since the stories are all multi-part arcs these days -- and Superman always wins. So the rest of the time, Metropolis is probably the safest city on the planet, since Superman's probably arrested or scared out all the run-of-the-mill criminals by now. (A while ago, I read a blog post commenting about the Superman comics of the '50s and '60s that were mostly about Superman playing inexplicably jerky pranks on his friends or getting involved in bizarre supernatural situations, and suggesting that the reason for that was that Superman had already succeeded in defeating all the actual
crime in Metropolis.)
...how the hell is Joker still allowed to live?
Because he's insane. I don't think the law allows for the execution of mentally incompetent people.
Besides, whenever the Joker does appear to get killed in the heat of conflict, he always survives somehow. So it's not so much that he's allowed to live as that he just keeps on doing it anyway.
...to that continuation, why is Lex Luthor able to regain power over and over again, complete with the public's trust?
Oh, that's very true to life. Look at all the banking executives who screwed over the country a few years ago and are still running their companies. Heck, look at the Republican Party. The worst economic crisis since the Depression happened on their watch, as a result of their policies, and yet only two years later they've been voted back into power.
...if the DC Heroes already met happy-go-lucky travellers from the future - Legion of Super Heroes - then doesn't it mean all is well in the end? In that case, can't they go on some form of vacation?
No, because they know that the reason it turned out well is because they didn't stop doing their jobs. Also because they know that history can be changed by superheroes punching walls and stuff.