The X-Men are part of the Marvel Comics lineup. They have their own unique place within the Marvel multiverse, with a dedicated fan base and a significant impact on the comic book world.
X-Men is not associated with DC Comics. It's a Marvel creation. DC and Marvel have their own unique superheroes and comic book worlds that are independent of each other.
Yes, there are many. You can find some on popular fanfiction websites like Archive of Our Own. Some explore Harley's complex relationship with Batman, often delving into her chaotic nature and how it interacts with Batman's sense of justice.