Uh, you're never going to get a story from either Marvel or DC that doesn't cut away from the "bad parts" because Marvel and DC are large corporations whose comics are still "marketed" to minors (even if those minors are like 17-years-old). So you're not going to have an in-continuity version of Superman ripping someone's head off, unless of course it was from a Black Label-type book. That doesn't mean Superman hasn't done "adult" things. For starters, it's heavily implied that he made a sex tape with Big Barda. Also, a recent Superman comic literally just cut to Lois and Clark in what is clearly a "post-coital" scene.
So, yeah, Superman is not really marketed only to children anymore. So writing the character as if he is is not good business.
And again, the capacity to do something is not the same as the authority to do something. How many times does that need to be explained to you?
Oh my god, no, it's not. For one, it would only really be a questioning of a state's sovereignty if we assumed that Clark was acting as an agent of another government. Secondly, simply crossing a border is not the same as literally laying claim to territory. That shouldn't require explanation.
Again, it is their business because rocketing a major U.S. city into the sky would have a major impact on regional and national commerce. Like, do you honestly not see the impact that that would have?? Imagine if New York all of a sudden decided it wanted to form its own independent city-state. That would obviously be a huge blow to the national economy, given that New York is the largest city in the country and the epicenter of so many of the country's largest industries. So, yes, it would cause trouble to others outside.
Then, of course, you have the fact that Metropolis is still U.S. territory. Like, for the millionth time. It is illegal under international law for anyone to just up and steal territory from a nation-state. If a certain number of citizens of Metropolis want to go found a floating city with Superman, they can leave the U.S. and build their own city. Nothing is stopping their physical being from leaving. They are just not able to take the physical location of Metropolis with them.
So, you're saying he is above out entire system of government? He is too good for the literal thing that we've built our entire society around: law and order? Yeah, again, that doesn't sound like Superman. That sounds like a self-appointed god-king, but it doesn't sound like Superman. I don't know who you've been reading but its not Superman.