Well, they're attacking Billy because they assume he's invading Khandaq, not realizing he only went there to scatter Black Adam's ashes. Same reason why the Khandaq troops attack Billy earlier (although Billy was an idiot for thinking him going into a sovereign nation without repercussions, especially since tensions are already high what with Superman and Wonder Woman going to Khandaq in issue #20).

Doctor Light powers appear to be absorbing light and/or electromagnetic radiation which he can expel in energy blasts, and he obviously doesn't have full control over his powers; this also explains why it appeared Superman "murdered" Doctor Light because it was really Doctor Light absorbing Superman's heat vision, which also explains why Superman doesn't understand what happened because he wasn't actively trying to use it. But of course, Wonder Woman is going to assume Pandora was responsible given how he went nuts when he tried to open the box.

Also, I don't think the Question is evil but more of an anti-hero who operates on his own code of what he thinks is justice, whether anyone else agrees with him or not.

As for why everyone is a gigantic asshole and fighting each other? Well, that's because they have to be in order for the entire plot to work, since actually trying to talk to each other to figure out what's going on right from the start would be too easy. ;-)