One possible plot development could be that Minato uses the knowledge of Naruto's past to help him train better. Maybe he reveals some hidden family jutsu or techniques that Naruto can use to become even stronger.
Well, first of all, Minato would likely be shocked. Naruto's past was full of hardships and loneliness. Minato would probably experience a mix of emotions. He might be sad that Naruto had to endure so much pain. He could also be proud of how Naruto overcame all those difficulties and still managed to grow into a strong and kind - hearted person. He might even try to find ways to comfort Naruto in this fanfiction world, like giving him some long - lost family memories or advice that could have made his journey easier.
In the 'bardock sees goku as a god' fanfiction, a plot development could be that Bardock's belief in Goku as a god gives Goku new powers or a new level of confidence. This could lead to Goku taking on more dangerous foes. Or perhaps Bardock tries to build a temple or shrine for Goku. There could also be a conflict where some villains try to use Bardock's blind faith in Goku to their advantage by tricking him into leading them to Goku.
One possible development is that Naruto becomes more composed. Minato was calm under pressure, and Naruto could inherit this trait. He might also become more of a loner at first as Minato was often on solo missions. But as he grows, he would learn to balance this solitude with his need for friends. His leadership skills would improve too, as Minato was a great leader.
One possibility is that Naruto's friends launch a rescue mission. They would use their unique skills, like Sasuke's Sharingan or Sakura's medical ninjutsu combined with her combat skills, to find and save Naruto.
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.
One possible plot development could be that Naruto discovers his deafness gradually and has to hide it from his enemies. He might be afraid that they would use it against him in battle. Another could be that his friends find out by accident and have to learn sign language to communicate better with him.
Well, one possibility is that Naruto's new Sharingan power could give him an edge in battles against stronger foes. He might be able to quickly analyze their moves and counter them more effectively.
Perhaps Naruto, as Katanas' nephew, gets involved in a conflict that dates back to the family's past. For example, an old feud with another ninja clan. And he has to use his skills and new - found family knowledge to resolve it. He might also learn some special sword techniques from his family connection to Katanas.
If Naruto were Samui's brother in fanfiction, it would likely lead to some interesting character interactions. For instance, Naruto might have a closer bond with the Cloud ninjas. He could also get involved in resolving internal issues within the Cloud Village. Maybe he would be more welcomed in the Cloud Village than in the original story. Additionally, it could affect his relationship with Sasuke, as he might have a new support system in the form of Samui and her comrades.
Itachi might start to question his loyalty to the Akatsuki after meeting Minato. Minato's strong sense of justice and love for his village could make Itachi re - evaluate his own actions.