One idea could be a crossover where Batman Beyond teams up with the Teen Titans to face a new threat in Gotham. Maybe a powerful villain has emerged who is using advanced technology that only Batman Beyond can understand, and the Titans' unique powers are needed to combat the villain's minions.
Batman could meet Starfire. She has unique powers and a different perspective from Batman. They might have a conversation about her powers and how she can use them more effectively. Also, Batman might be curious about her alien origin and what it means for the Titans' capabilities.
There probably is. Given the popularity of both Darkseid and Batman in the DC universe, it's a common and rather dark theme for fanfiction writers to explore. Some might write it to show the extreme power of Darkseid, while others may use it as a starting point for a more complex alternate universe story where Batman's death has far - reaching consequences for other characters.
One interesting plot could be that Percy has to face an ancient and powerful Titan that has been awakened from a long slumber. He uses his unique water powers in unexpected ways, like creating a giant water vortex to trap the Titan and then using his sword to deliver the final blow. Maybe he also teams up with some unlikely allies, such as a group of minor gods who have a vendetta against the Titans.
I don't think it's a common concept. Most Batman fans love the character for his moral code which includes not killing. Fanfiction usually tries to expand on the existing lore in a way that is somewhat in line with the general perception of the character. So, stories where Batman kills are more of an exception rather than the norm in the fan community.
Batman's origin in Teen Titans Go is somewhat of a comical take on the traditional origin. He witnessed the death of his parents in Crime Alley which drove him to fight crime. But in the Teen Titans Go version, it's presented with their signature humor.
In the fanfic, Batman might use his advanced gadgets to save the Teen Titans. For example, he could use his grappling hook to pull them out of a dangerous situation like a collapsing building. His Batmobile could also be used for a quick escape or to ram into villains threatening the Titans.
In some fanfics, the moment when the Teen Titans and Batman Beyond combine their powers to defeat a seemingly invincible villain is always a highlight. For instance, if the villain has the ability to absorb energy, the Titans use their powers in a coordinated way to distract the villain while Batman Beyond figures out a way to disrupt the villain's power - absorbing mechanism.
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.
In a 'batman kills fanfic', it's a deviation from the norm. Fanfics often play with established characters in new ways. Here, Batman killing might be used to create a shock factor or to tell a story that challenges the status quo. It could be set in an alternate universe where the rules are different. It might also explore the psychological impact on Batman himself, as killing would go against everything he stands for in the regular DC Comics world. It's a creative exploration by fans who want to see what would happen if Batman took a more lethal approach.