One great storyline could be them teaming up to solve a mystery in Gotham that the Bat - family has overlooked. Maybe a series of strange disappearances that seem to have no connection at first, but as they dig deeper, they discover it's all part of a grand scheme by a new villain. They would use their unique skills, Bat Girl's martial arts and detective skills, and Tim Drake's brilliant mind and acrobatic abilities to piece together the clues.
Another possibility is that Batman is experimenting with a new technology to enhance his abilities. He creates a device that is supposed to give him the ability to fly like a bat. However, something goes wrong during the testing phase. The device fuses with his DNA, and he starts to turn into a bat. He has to deal with the physical and mental changes, all while trying to keep it a secret from his allies like Alfred and Commissioner Gordon.
First, know the characters well. Read the comics or watch the shows related to them. Understand their personalities, like Bat Girl's determination and Robin's intelligence. Then, come up with an interesting plot. It could be something that challenges their relationship or their abilities. For example, a new villain who targets their weaknesses. Also, write good dialogue that sounds like how they would actually talk. Don't make it too out of character.
The Penguin could be a great addition. His wacky and devious schemes always make for an interesting story. Also, Catwoman. Her complex relationship with Batman adds a layer of intrigue. And Oracle, who can provide valuable information and support from afar.
One interesting storyline could be Robin growing up and struggling to step out of Batman's shadow. He wants to prove himself as an independent hero while still respecting Batman's teachings.
In many Batman and Robin fanfictions where Robin is injured, it often leads to Batman becoming more determined to catch the villain. For example, in some stories, Robin gets injured during a fight with a new, powerful enemy in Gotham. Batman then uses his detective skills to track down the bad guy while also taking care of Robin. He might call in Alfred for help with Robin's injuries. This kind of situation shows the deep bond between Batman and Robin and how they rely on each other in tough times.
Yes, it probably is. Batman has a huge fan base and graphic novels about him often offer unique interpretations of the character. This one might showcase different aspects of Batman, his alter - ego Bruce Wayne, and his adventures in Gotham City.
I'm not entirely sure as I haven't read this specific fanfic. But it could be about Robin documenting the rules that the Bat Boys (presumably Batman and his allies like Robin himself, Nightwing etc.) follow in their crime - fighting and vigilante activities.
There is no love story between them. Batman is more like a father figure or a strict mentor to Robin, guiding him in the fight against crime in Gotham City.