I'm new to the world of minecraft. I've had a Ender Dragon in my world with the command / summon ender_dragon. I expected this similar to eg. A phantom would fly through the air. But no. He flew criss-cross through the air to fly vertically through the map, destroying everything. Is that normal?
No, since the Enderdrache is not optimal for the normal world. The Enderdrachen you find legitimate in the final world.