Lois Lane on bad people deserving to die might just be seen as the writers trying to make her be a little at odds with Clark's view, until you realize her father is in the military and that she would have grown up with such a viewpoint, then it makes perfect sense.
Just to point out, Lois says that 'sometimes' she feels that way. She seems to mean it as a 'heat of the moment' or 'in a moment of weakness or anger' thing. She's actively trying to stop the crowd from supporting the Elite when they hold Atomic Skull's impromptu execution.
Manchester Black proves himself capable of fighting on (mostly) even terms with Superman during his Beware the Superman phase. If Superman hadn't simply been acting, then no matter who won the battle, it's safe to say that the entire world would be several kinds of screwed.
Not really, Supes was still clearly holding back. Had he genuinely wanted to kill the Elite, he would have beaten them, taxidermied them and put on an insulting marionette show with their corpses in the span of 2 seconds.
You can tell that Supes didn't ever really use his super speed other than to dodge attacks. If he really wanted Black dead, he woulda been punching alot faster.
Yeah, but it's obvious that they were doing damage to him. And Manchester was correct at the end that Superman could barely stand after his last telekinetic blast. You gotta remember, Superman is incredibly strong and can take a lot of damage but he's not invincible.
Keep in mind, Superman didn't beat any of them through brute force. While the comic version showed it more, all of the Elite except for Menagerie had the power to beat Superman on their own. The comic version of Coldcast was explicitly said to have far more power to throw around than Superman. Even if he was holding back, during the head-to-head part of the fight Superman was still injured far worse by them than the Atomic Skull. If they'd taken the fight seriously instead of treating it like a Payperview event, things would have gone very differently.
But then, if they were the type to think things through and treat their enemies with respect, it would have been a very different story.
Superman reveals that he didn't actually destroy the part of the brain that gives Black his powers, but since the Elite is going to be de-powered anyway, what difference does it make?
That's part of Superman's point: Maybe the authorities decide to de-power them. But it's not Superman's place to make that decision.
Also, Superman's heat vision would have set fire to Manchester's eyes rather then just one part of his brain if he tried to do that.
Better question: if the ability to depower someone exists, and it is in the hands of the authorities, why are there repeat offenders of super powered criminals?
Perhaps, like with the Atomic Skull as a power source, some government officials believe they can use the Supercrimnals as a resource.