Even when your heart breaks to do something in the moment, it doesn't mean that you carry it with you for days to the point that it negatively affects your ability to function as a hero for the world or for the protection of the people in your own life who could be hurt if the government's spy drones revealed his secret identity. He also needs to approach a new situation with the right demeanor; he can't very well confront Swanwick while still teary eyed over Zod's death. Moreover, as upsetting as it was, it was a decision that he made. I doubt he regrets the killing so much as the fact that the situation got to that point where there were no other options. Which is why seeing Superman choose to take Doomsday out of the city and into space and sacrifice himself are indicative of his growth in terms of learning from his mistakes. As for the rest, I don't know what movie you saw, but no version of BvS features Superman killing anybody. If you're referring to Doomsday, Superman always kills Doomsday, and Doomsday is not alive. He's like a zombie. Explain to me your righteous morality and justice. Tell me, if you had to choose a villain dying to save millions of innocent people, would you choose the villain's life and preserving your own self-righteousness over those innocent lives?
Since Superman killed both Zod and Doomsday in the comics, I wouldn't say it's not something Superman would ever do. I also wouldn't put Zod and Doomsday on the same level. Zod was a sentient and living thing. Doomsday was neither; he was a zombie. He was all instinct and no thought or emotion. What do you propose, though, that Superman could have done differently with Doomsday? If there isn't a better way, then are you suggesting that Superman can only be Superman and that morality can only be upheld when the world is made easier for you? The real world isn't like that, and morality that isn't tested isn't indicative of morality at all. A Superman who has another option given to him by the narrative is a Superman who is allowed to escape the test and the consequences of having to make a moral decision. It becomes abstract virtue, which is meaningless. So, ask yourself, what is the moral choice in a circumstance with no easy answers?
Superman's been destroying government property and sticking it to the man since his inception. I believe even Reeve's Superman did so when he gathered a bunch of nukes and threw them into the sun. And flying faster to not be tracked? That seems odd, especially since there has to be times when Superman can't do that because he needs to take his time. It doesn't sound practical, and it ignores the principle of the thing, which is that the government shouldn't spy on Superman. Their relationship needs to be built on trust.Superman isn't supposed to go around destroying government property though, that would just make people afraid of him. Besides in the comics Superman just flies faster than he can be tracked which is something Cav-El has yet to figure out.
Again, not two villains. He also didn't kill the warlord, and that's made clear by his denial to Lois that he didn't kill anyone in Africa. Superman's approach to Batman isn't as clear cut as you're presenting it. Superman says that Lex presented the dilemma as save Martha or kill Batman, but Superman decided to alter that a bit to getting Batman to save Martha or kill Batman. However, knowing what the options are doesn't mean that they are ones you're willing to do or go through with. Superman approaches Batman with humility, apologizing and trying to reason with him. Even in his dying breaths, he was trying to reach Batman. He even says at one point that if he wanted it, Batman would be dead. He didn't want that.Pahahaha saving Lex makes up for killing two villains in a row? Right after he was willing to kill Batman to save his mother? And possibly killed an African warlord threatening Lois? Please the moral bankruptcy in Cav-El could have funded the DCEU ten times over. If the future of Superman fans are those introduced to an emo, moody, self depreciating dead wood collataral destroying murderer, the next generation of Superman fans will ruin everything the character stands for.
In short, I disagree with what I feel are hyperbolic criticisms of this character and these movies.