3) Why Would Anyone Think A Nuclear Strike Above A Major City Is Safe?
Nukes. They can do major damage, but as long as you detonate them safely a couple of miles away, there’s absolutely no chance of problems for those on the ground. That’s nonsense of course, but in Batman V Superman this is inexplicably apparently accepted logic. As Superman and Doomsday battle in the sky above Metropolis, it takes the American government all of half a minute to decide that exploding a nuclear device over the city is the right thing to do.
The explosion’s close enough that the people of Metropolis can see it (the flash of which would very likely blind them, FYI), and large enough that the shockwave at the least would be felt down on the ground. The most dangerous consequence, though, would be nuclear fallout: Metropolis may be out of immediate harm’s way, but thanks to gravity the city would be due a shower of radioactive fallout that would turn it into America’s Chernobyl.