Well, it depends on the specific fanfiction. Some fanfictions might make Naruto Tobirama's grandson to explore new storylines. For example, they could use this relationship to explain Naruto's strong chakra or his natural leadership skills. It could also be used to introduce new conflicts or alliances within the Naruto world that are not present in the original series.
Yes, there could be such fanfics out there. Fanfic writers often come up with creative family relationships that deviate from the original Naruto storyline. They might explore how Naruto's character would be different if he had such a relation to Tobirama. Maybe in these fanfics, Naruto could inherit some of Tobirama's unique jutsu or characteristics, which would add a whole new dimension to his character development and the overall story.
One consequence could be a change in how Naruto is perceived in the village. Since Tobirama was an important figure, Naruto might be held to an even higher standard. Also, it could affect Naruto's relationships with other characters. For example, some might be more deferential to him.
Perhaps in this fanfiction, there's a secret prophecy about Naruto being the grandson of Madara and Tobirama. This leads to a lot of political intrigue within the village. Some people want to use Naruto for their own gain, while others are afraid of what his true heritage might mean for the future of the Hidden Leaf.
Yes, there are quite a few. You can start by looking on popular fanfiction websites like FanFiction.net or Archive of Our Own. Just search for 'Naruto grandson of Tobirama' and you'll find a variety of stories with different plotlines, some might focus on his relationship with the Hidden Leaf Village, others on his unique jutsu inherited from Tobirama.
One possible plot could be that Naruto discovers his relation to Tobirama later in his life. This new knowledge makes him strive to learn more about his ancestor. He might search for Tobirama's hidden techniques and knowledge. Along the way, he could face opposition from those who don't want him to gain such power, thinking it would disrupt the balance in the village.
There could be a backstory where Madara and Tobirama had a secret agreement that led to Naruto's existence. Maybe they foresaw a future threat and planned for Naruto to be born with their combined power to save the ninja world. Naruto would then have to uncover this mystery and fulfill his destiny.
One plotline could be Naruto having to deal with the expectations and legacy of Tobirama. Since Tobirama was a great shinobi and one of the founders, Naruto might feel pressured to live up to that. Another could be the discovery of this lineage leading to new enemies targeting him.
The plot could involve Naruto exploring the history of the Senju clan through Tobirama. Maybe there are secrets or prophecies related to the Senju that Naruto is now a part of. This could lead him on a quest to uncover the truth about his family and the clan's past, all while still dealing with the regular threats to the Hidden Leaf Village.
In this fanfiction, Naruto might have a natural affinity for Tobirama's administrative skills. He could use these skills to improve the village in ways he hadn't thought of before. For example, he could implement new training programs for the ninja academy based on Tobirama's ideas. Additionally, there could be a sub - plot where Naruto has to deal with a group of ninja who oppose his new - found influence because they are afraid of the power that comes with being related to Tobirama. This could lead to some intense battles and political intrigue within the village.