Hinata would be heartbroken at first. Naruto is someone she deeply cares about. But she's also a strong - willed ninja. So she might start by trying to understand why Naruto left. She could look for clues in the village or talk to Naruto's friends to figure out his possible destination.
Hinata would likely go to great lengths to save Naruto. She might seek help from the most powerful medical ninjas in the village or even venture out to find a rare herb or a mysterious healer. She would be in a state of shock at first, but then her love for Naruto would drive her to take action.
In some fanfictions, Naruto is completely oblivious at first. He doesn't understand why Hinata is acting strange. He just goes about his day, being friendly as usual. But as Hinata's jealousy becomes more obvious, he might start to notice that something is wrong. He could be confused and try to ask Hinata what's bothering her.
Hinata might be shocked at first. She is a gentle soul, so seeing Naruto be so violent towards Sasuke would be unexpected. But then she would probably try to stop Naruto, as she doesn't like to see people fighting. She might also feel a bit guilty, thinking that her relationship with Naruto somehow caused this conflict between the two friends.
I'm not sure if there is such a fanfic. Cheating storylines in fanfics can be quite controversial as they go against the positive relationship often depicted between Naruto and Hinata in the original work.
Communication is key. Naruto needs to sit down with Hinata and have an honest conversation about what's going on. He should explain his actions and feelings clearly.
In some Naruto fanfictions where Naruto hurts Hinata, it could be due to a misunderstanding. Maybe he's under some sort of mind - control or false information has been fed to him. This often leads to a lot of angst in the story.
It's an interesting but also a bit of a disturbing concept. On one hand, fanfics are a place for creative exploration. But on the other hand, the naruhina relationship is so beloved that a cheating plot might make a lot of fans unhappy. It could also be seen as a way to add some dark drama to the story, but it's not in line with the positive and hopeful tone of the original Naruto series.
Hinata would be overjoyed. She has loved Naruto for a long time, so his proposal would be like a dream come true for her. She might start crying tears of happiness and immediately say yes without hesitation.
Hinata might be very hurt. She's a sensitive person, so Naruto yelling at her could make her feel small and sad. She might start to doubt herself and her abilities.