One possible reason could be mind control. Maybe some villain has taken over Superman's mind and made him do it. Another reason might be a fundamental difference in their ideologies that has escalated to the point of no return.
Yes, there are some out there. You can start by looking on popular fanfiction websites like Archive of Our Own or FanFiction.net. Just search for the specific tag'superman kills batman' and you'll find a variety of stories. However, the quality can vary greatly from one to another.
Yes, there are likely some out there in the vast world of fanfiction. Fanfiction writers often come up with unique and unexpected crossovers like this. However, the quality and popularity can vary greatly.
Lois Lane is often a popular character. In fanfiction, she might play a crucial role in mediating between Batman and Superman or getting involved in their adventures in a more hands - on way, using her investigative journalism skills.
Alfred Pennyworth is quite popular too. He can offer his wisdom and support to Batman, and his interactions with Superman can be both humorous and heartwarming. He's like the glue that holds things together in the Batcave, and his presence can bring a sense of home to the story.
It's more modern in terms of art and storytelling. The New 52 version has a different aesthetic compared to older comics. It often has a faster - paced plot.
Lex Luthor is often an interesting character in such fanfictions. He might be the one pulling the strings behind the scenes, fueling Batman's distrust of Superman. Another could be Alfred. His wisdom and influence on Batman can add depth to the story. He might try to talk Batman out of fighting Superman or help him in a more covert way. And then there's Wonder Woman. She could be caught in the middle, trying to mediate between the two or having her own motives for getting involved in their conflict.
Catwoman can also be a popular character. She could be in a love - triangle situation with Batman, and her thieving ways might put her at odds with the female Superman who stands for truth and justice. There could be some really interesting interactions between the three of them, like Catwoman trying to steal a valuable item that the female Superman is protecting, while Batman is caught in the middle, not sure who to side with at first.
Wonder Woman could also be involved. She might be caught in the middle, trying to stop the fight at first. But if she realizes that Superman is being a threat for some reason, she could side with Batman, or at least not interfere in Batman's attempt to defeat Superman.