In a fanfiction where Naruto and Hinata are stuck in the past, one possibility is that they would be seen as strangers at first. Naruto's unique abilities and Hinata's gentle yet strong presence would attract attention. They could end up being involved in some of the key historical events of the ninja world in different ways. Naruto might try to change the outcome of some battles, while Hinata could use her Byakugan to uncover secrets that were lost in the original timeline. This could lead to a whole new series of events and relationships, and might even change the future they came from in unexpected ways.
They might try to change some past events. For example, Naruto could prevent some of the early tragedies in the village. Hinata might also get the chance to be more assertive earlier in her life, since she has Naruto by her side this time. They could also have an impact on the relationships between different ninja clans.
Another thing that could occur is that they encounter some strange creatures or phenomena inside the box. Naruto would be ready to fight, but Hinata might first try to understand the nature of these things. They'd have to combine their different approaches to deal with the situation, and in the process, their relationship would evolve, whether it's becoming better friends or something more romantic.
They could use their ninja skills to try and break out of the box. Naruto might try his Rasengan, while Hinata could use her Gentle Fist to find weak points in the box's structure.
Well, if Naruto and Hinata go to the past in fanfiction, it could be really interesting. They could meet their younger selves. Naruto might see his lonely childhood self and try to give him some hope. Hinata could also see her shy younger self and perhaps encourage her to be more confident earlier. And they could also influence the relationships between other characters. For instance, they might help their friends' parents get together or something like that.
Their relationship could develop more quickly. In the past, without all the distractions and responsibilities of their original time, they could focus more on each other. Hinata might be more confident in expressing her feelings earlier, and Naruto would likely be more receptive since he's away from his normal hectic life.
In this fanfiction situation, they could end up using their knowledge of the future to help people in the past. For example, Ash could use his Pokémon training skills to solve some problems that people in the past were having with wild Pokémon. Serena could perhaps use her cooking skills to introduce new recipes. And together, they would be constantly looking for clues or a magical item that could send them back to their time.
In a Naruto and Hinata date fanfiction, they could start their day by visiting the memorial stone. Naruto would tell Hinata about his friends who sacrificed themselves. Then they would take a walk in the forest, holding hands and enjoying the peaceful nature around them. Hinata might shyly give Naruto a flower she picked along the way.
There could be a scenario where Kushina comes back to life somehow in the fanfiction. She might then play matchmaker between Naruto and Hinata, using her knowledge of Naruto to help Hinata understand him better. For example, she could share stories of Naruto's childhood that would make Hinata feel closer to him.
It could also result in a change in the way the village views their relationship. Since Naruto is a hero, his saving of Hinata would be a big deal. This could lead to the village elders or the people in general being more accepting of a possible romantic relationship between them. For example, they might start to see Hinata as a more important figure in Naruto's life and give her more respect.
Well, in a 'naruto absorbs hinata fanfiction', Naruto could absorb Hinata's gentle and kind-hearted nature along with her skills. This might change his personality a bit, making him more empathetic. And perhaps he could use Hinata's family techniques in a new and creative way, like combining the Gentle Fist with his Rasengan.
Perhaps in the fanfiction, there's a tournament or a competition. Naruto would be eager to prove himself, Hinata would be quietly determined, and Renamon could show off her combat skills. Their interactions during the event could lead to new friendships and rivalries. They might also learn new techniques from each other during the process.