The plot might go like this. Slade kidnaps Robin in a very stealthy way. He takes Robin to an abandoned building. There, he tries to indoctrinate Robin into his way of thinking. He could be telling Robin that Batman is using him and that he can offer Robin more power. However, Robin stays true to his beliefs. Meanwhile, Batman is on a frantic search for Robin, following every lead, and the Bat - family is also on high alert. Robin is constantly looking for an opportunity to turn the tables on Slade and escape.
The other Teen Titans could also play a big role in the rescue. Starfire could use her powers to fly in and distract Slade while Cyborg and Beast Boy create a diversion. Raven could use her magic to break any spells or traps that Slade has set for Robin. They would all work together as a team to get Robin back safely.
He may also try to talk his way out. Nightwing is known for his charm and intelligence. He could try to reason with Slade, find some common ground, or play on Slade's emotions. Maybe he could remind Slade of a past event where they had a moment of mutual respect, hoping to make Slade let him go.
One possible motive could be revenge. Maybe Nightwing has thwarted Slade's plans in the past, and Slade wants to get back at him. Another could be that Slade sees Nightwing as a valuable asset. He might plan to use Nightwing's skills for his own evil purposes, like forcing him to steal something or gather information for him.
Yes, there are likely some out there. You can start by looking on fanfiction websites like Archive of Our Own or FanFiction.net. Just search for 'Slade hurts Robin' and you should be able to find relevant stories.
Robin would probably stay calm and observant. He's been trained well, so he'd immediately start looking for any weaknesses in his captivity situation. He might try to pick the locks on his restraints if he's bound, or find a way to communicate with his team secretly if there's a chance.
One common theme could be the power dynamic between Slade and Robin. Since Slade is often portrayed as more powerful and experienced, it creates an interesting dynamic in the fanfiction. Another theme might be the forbidden nature of their relationship, considering their different sides in the story's context.
In this kind of fanfiction, Robin might be in a lot of danger. Slade could be using Robin to get to Batman. He might try to brainwash Robin and turn him against his friends. For example, he could lock Robin in a secret lair and show him false information about Batman to make Robin question his loyalty.
Nightwing could also be a likely savior. He was once Robin himself and has a strong bond with the current Robin. He might take it upon himself to rescue Robin, using his own unique fighting style and experience to outwit the Joker. Plus, he has his own network of contacts in Gotham that could help in the search.