You know where Doomsday came from. Zod and Lex DNA mixed together.
No point to Wonder Woman. She just happened to be in town.
People don't ask how Superman survived cause people know Superman is Superman.
There was commentary by the government on how the nuke would kill Superman and they did it anyway. He is seemingly killed like they predicted, revived by the sun and you don't hear anything (amazement, bewilderment) from the military. In fact, you don't hear anything from the military again because they have seemingly given up on trying to fight Doomsday, which doesn't make any sense at all given how big of a threat he is.