Well, if Harry and Dudley became friends, it would drastically change the whole dynamic of the early Harry Potter story. For one, Harry might not have felt so alone at the Dursleys' place. Dudley could have protected Harry from Vernon's wrath. Also, they could have shared secrets about the wizarding world with Dudley being a Muggle. This new friendship might even have led to Dudley developing an understanding and acceptance of the magical world much earlier, and perhaps he could have been an ally to Harry in the fight against Voldemort, instead of a bully.
They could have adventures in the Muggle world. Maybe they would explore abandoned places in their neighborhood. Dudley, with his knowledge of the local area, and Harry, with his courage and magic (if he could use it secretly), could discover hidden treasures or solve mysteries. For instance, they might find an old diary that has some connection to the wizarding world but was lost in the Muggle world long ago.
Harry might become more open and less guarded. Since he now has a brother in Dudley, he might feel more at home in the Muggle world. Dudley, on the other hand, could become less of a bully. The knowledge that he has a wizard for a brother could make him more humble and empathetic.
It could lead to a big change. Maybe Harry and Dudley would learn more about Severus and develop a different relationship with him.
It could develop after a major event changes Dudley's perspective. Say, Dudley witnesses the true extent of the danger Harry faces in the wizarding world. This could make him feel protective of Harry. He might start to defend Harry against their parents' unfair treatment. And Harry, seeing Dudley's change, would be more open to being friends. They could then start to communicate more, sharing their hopes and fears, and slowly but surely, a friendship would form.
One way could be to have the Cartoons Ninja be a magical being from a different dimension that has the ability to cross into the Harry Potter universe. Dudley could encounter this ninja first, thinking it's just some new strange thing in his muggle world. But then it turns out the ninja has a connection to Harry's world. Maybe the ninja is on a mission to find a powerful magical item that Harry also needs, and Dudley gets caught in the middle.
In this fanfiction, perhaps Dudley's envy of Harry's magical world finally boiled over into uncontrollable rage. He might have found a way to cross into the wizarding world without anyone knowing. And in a moment of extreme jealousy and anger, Dudley could have used some kind of weapon or spell (maybe through some dark magic loophole) against Harry, which unfortunately led to Harry's death. Fanfiction allows for these extreme and unexpected plot twists.
Sure. Fanfiction often takes the existing characters and situations and twists them. For Harry and Dudley, it could start with a shared experience that makes Dudley realize Harry isn't so bad. Maybe they get caught up in a magical adventure together outside of the normal Hogwarts - related stuff. This common experience could break down the barriers between them and start a friendship.
It could lead to different alliances. Harry might form new friendships or partnerships that he wouldn't have in the original story. This could change the power dynamics in the wizarding world. For example, he might team up more with Hermione alone, and their relationship could develop in a different way, perhaps more romantically earlier since they don't have Ron as a buffer.
In this fanfiction concept, the story would be turned on its head. The whole mystery around Harry's parents and his connection to Snape would be reimagined. Their shared heritage as twins could lead to new magical abilities that they discover together. The Hogwarts houses might even treat them differently. For instance, Snape being a Slytherin and Harry being a Gryffindor in the original, but as twins, there could be a whole new dynamic within the houses. And the final battle with Voldemort could be fought in a completely different way with their combined strength and new - found relationship.
One possible plot twist could be that Dudley discovers he has some latent magical ability. This would completely change their dynamic as Dudley has always been the 'Muggle' bully. It could lead to him having to rely on Harry for guidance in the wizarding world, which in turn would force them to become friends as they navigate this new situation together.