Superman is definitely a DC Comics character. DC has built a rich and extensive mythology around him over the years. He's a symbol of hope and justice in the DC world.
Yes, there are quite a few. Some fanfiction writers like to explore what would happen if Superman entered the Marvel universe. For example, they might write about Superman teaming up with the Avengers to fight a common threat. It's interesting to see how his powers would compare to those of Marvel characters like Thor or Hulk.
Well, AO3 is a great place. It has a well - organized tagging system. So if you search for tags related to DC, Marvel, and Superman, you should be able to pull up relevant crossovers. Additionally, some specialized comic - related forums might also have links or discussions about such fanfiction. However, make sure to follow the rules of those platforms.