You can start by looking on popular fanfiction websites like Archive of Our Own (AO3). It has a large collection of fan - created works, and you're likely to find many 'Batman loves Superman' stories there. Just use the search function and type in relevant keywords.
Yes, there are quite a few. Some fanfictions might explore their complex relationship in different universes, like a world where they have to team up against a greater threat and develop a deeper bond during the process.
One great 'Batman loves Superman' fanfiction could be one where they team up against a common enemy in a way that shows their deep bond. For example, a story where they face a powerful new villain who is able to manipulate minds. Batman uses his detective skills and Superman his super strength to overcome the mind - control and in the process, they realize how much they rely on each other and their feelings grow deeper.
Fanfiction.net is also a good place. There are likely to be numerous stories about Superman loving Batman there. Just use the search function and look for relevant tags.
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.
Well, it could imply that Superman has an interest in Batman fan - created stories and is willing to be associated with them. Maybe in this fanfic universe, Superman has a special connection to Batman's story world.
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.
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.
In fanfiction, Batman and Superman's friendship is often complex. They are two very different heroes. Batman is a brooding, human with no superpowers but great intellect and skills. Superman is an alien with god - like powers. Their friendship can be based on mutual respect for their fight against evil. Sometimes Batman is the one to keep Superman grounded, reminding him of his humanity. And Superman, in turn, can show Batman that there is more to the world than just the dark alleys of Gotham.
Pink kryptonite in fanfiction related to Superman and Batman can add a touch of the unexpected. It's not a traditional element from the main DC canon. Fanfic writers might use it to make Superman more vulnerable in a different sense than the usual kryptonite. And Batman, being the strategist, could use this situation to his advantage in the story, perhaps to gain some upper hand in their often - complex relationship.
In Batman and Superman fanfiction, 'stranger danger' can be depicted in various ways. For example, a new villain could be introduced who is a stranger to the city and poses a great danger. The heroes would then have to figure out the stranger's motives and powers to stop them. It adds an element of mystery and suspense to the story.