There's also 'Batman: Under the Red Hood' which, while not directly about the initial 'Joker kills Robin' event, still touches on the aftermath. It shows how the death of Robin haunts Batman and how it affects the actions of other characters in the Batman universe. It also gives more insight into the Joker's psyche and his role in Robin's death.
It made the Batman universe much darker. The death of Robin was a huge shock, and it changed Batman's character. He became more brooding and intense. It also showed how dangerous the Joker really was, not just as a villain who commits crimes, but as one who can cause such personal and emotional harm to Batman.
Robin would probably be both scared and angry. He's a brave kid, but facing the Joker alone is no small feat. He might initially try to fight back if he has the chance.
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.
Robin does not become the Joker. The characteristics and roles of these two characters are completely different. They exist within separate story arcs and have no direct transformation connection.
I'm not entirely sure which specific 'Joker graphic novel' you mean. But generally, the Joker's kills are often brutal and random. He might kill for fun, to prove a point, or just to create chaos.
It's a really wild idea. On one hand, Naruto has the power to take on the Joker. His chakra abilities like the Rasengan could potentially be a deadly weapon against the Joker. But on the other hand, the Joker is a master of psychological warfare, which Naruto may not be used to dealing with. In a fanfiction, it would be fascinating to see how the writer would make these two characters interact and how Naruto would ultimately defeat the Joker.
Maybe a family member of a police officer killed by the Joker. This civilian has a strong sense of justice and a personal vendetta. They are not bound by the same rules as the police and are more likely to take extreme measures. They have seen the destruction the Joker has caused to their family and will stop at nothing to get revenge.
One common theme is chaos. With Batman gone, Gotham descends into utter chaos as the Joker runs amok. Another theme is revenge. Sometimes the story is about someone seeking revenge for Batman's death. Also, the exploration of the Joker's victory is a theme, showing how he relishes in finally killing his nemesis.
There are some out there. Some explore the dark and twisted nature of such a scenario, delving into the psychological impact on Gotham and the other characters. However, the quality can vary greatly. Some might focus more on shock value while others try to build a complex narrative around it.