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.
Nope, Superman isn't a Marvel comic. He's a key figure in the DC Comics world. DC has its own unique style and set of characters, and Superman is a big part of that.
Superman could fit into the Marvel Universe in several ways in fanfiction. Firstly, his origin could be tweaked a bit. He could be an experiment gone wrong in a Stark Industries lab that gave him his powers. This would immediately connect him to the Marvel world. His powers would still be his trademark ones like flight, super strength, etc. He could then become a sort of protector of a particular city in the Marvel Universe, like New York. He would interact with the local heroes and villains. His presence would disrupt the power balance a bit, and some villains might target him specifically. But with his unwavering moral compass, he would stand up to them and become an important part of the Marvel Universe's tapestry of heroes.
Well, it could be interesting. Superman has his own unique set of powers and characteristics. In Marvel fanfiction, it could lead to some really cool crossovers. For example, imagine Superman facing off against Thor. Their strength levels are somewhat comparable, and it would be a battle of two powerful beings from different universes. However, it might also be a bit tricky to blend Superman's DC lore into the Marvel universe without some contradictions.