In some fanfictions, Deidara might give Naruto training on explosive jutsu control. Since Deidara is known for his explosive clay techniques, he could potentially teach Naruto how to better handle and utilize explosive elements in combat.
In many 'naruto female deidara fanfic', the female Deidara often has a more nuanced personality. She might be more empathetic than the male version. For example, she could show more concern for the villagers affected by her explosive art.
Gaara would be an interesting character to include. Since he has his own experiences with being an outcast and finding his place in the world, he could relate to Deidara in some ways. And Gaara's sand powers could create some unique battle combinations with Deidara's explosive art. Rock Lee is also a great choice. His determination and unique fighting style of taijutsu could add a different dynamic to the story. He could also inspire Deidara with his unwavering will to improve.
One interesting 'Naruto and Deidara fanfiction' could be about them having to team up against a common enemy. In this story, Naruto might initially be distrustful of Deidara because of his past actions as an Akatsuki member. But as they face the new threat, they start to understand each other's fighting styles and develop a grudging respect. Deidara could use his explosive art while Naruto uses his shadow clones and Rasengan. They gradually learn to work in harmony to defeat the powerful foe.
In this fanfiction, it could also be that Naruto discovers a connection between Deidara and some ancient ninja art or prophecy. This discovery could lead him on a journey to uncover more about his supposed father's past. Along the way, he might encounter characters who knew Deidara and learn different aspects of his personality that were not known before. He could then use this knowledge to better understand himself and his place in the ninja world.
Obviously Naruto himself. Then there could be characters like Sasuke who might react differently to Naruto's newfound parentage. Sakura too, she might be concerned about how this affects Naruto and their team. Kakashi could also play an important role, perhaps guiding Naruto through the confusion of his identity. And who knows, some of Deidara's old Akatsuki comrades might show up to either help or harm Naruto depending on their motives.
Well, in a fanfiction where Naruto is trained by Deidara, Naruto's creativity in combat would probably skyrocket. Deidara is all about his explosive art, and Naruto could learn to use chakra in ways he hadn't thought of before. Maybe Naruto would start using the environment in a more explosive way during battles, like turning rocks into mini - explosives like Deidara does with his clay. Also, Naruto might have to struggle with Deidara's nihilistic attitude towards life at times, but it could also make him more empathetic towards enemies with different outlooks in the long run.
I'm not sure of a specific 'naruto deidara is naruto's brother' fanfiction, but generally in such a concept, the fanfic could start by exploring how they were separated at a young age, perhaps due to some sort of conflict between the Hidden Leaf and Iwagakure. Then as the story progresses, they could discover their relation in a very dramatic way. This could then lead to them having to choose between their existing loyalties (Deidara to Akatsuki and Naruto to Konoha) and their new - found brotherhood.
Perhaps there could be a plot development where other characters react to Naruto's training with Deidara. For example, Sasuke might be suspicious or even jealous of Naruto's newfound skills. This could create tension between the two characters and lead to some exciting confrontations.
One possible plot development could be that they initially fight against each other as enemies, not knowing their relation. Then, through some kind of accident or revelation, they find out they are brothers. This could lead to a lot of internal conflict for both of them, especially for Deidara who has been on the 'wrong side' in the eyes of Konoha. Another development could be that there is a third party who knows about their relation and tries to use it for their own gain, forcing Naruto and Deidara to work together to overcome this threat.