About the Kryptonian message - The Kryptonians are actually violent and are known to be conquerors. Their violence led to the destruction of their own planet, with Jor-El sending Kal-El to Earth so he has a chance to survive. That message saying he should rule Earth is pretty much what Kryptonians would do. But Clark grew up on Earth with amazing parents that's why he would never be like Kryptonians.
Some more facts:
1) This movie is heavily based on the comic "All Star Superman." Including the Robots as well as his costume.
2) The Supergirl's interpretation in this DC universe is based on "Supergirl: Woman of Tomorrow". She is a much darker character than Superman, which we will get to see in her own movie.
3) Ultraman is an actual Superman villain. He is an alternate-universe version of Superman and leads the Crime Syndicate in comics. In this movie they made him a clone of Superman.
4) Krypto is sometimes' Superman's dog and sometime Supergirl's dog in the comics based on different interpretations.
5) Alan Tudyk actually improvised the dialogue where he asks Superman to call him Gary :D
6) Hammer of Boravia was voiced by David Corenswet himself.