It can create a lot of tension. The other characters may start to avoid him, which can split the group. For example, if Toothless is also affected by Hiccup's mood, it can change their relationship dynamic. This can lead to new plotlines as the other characters try to figure out what's wrong with Hiccup and how to fix it.
One possible reason could be that he's under a great deal of stress. Maybe there are new threats to Berk that he's trying to deal with alone and it's getting to him. Another reason might be personal issues, like if he's having problems with his relationship with Astrid or his father. Or perhaps he's frustrated with the dragons not following his commands as he expects, which makes him lash out at everyone around him.
His friends might start to avoid him. If Naruto is constantly snapping at them, they'll feel hurt and not want to be around him as much.
If Astrid gets injured, it could strengthen her relationship with Hiccup. Hiccup would be very worried about her and would do everything he can to take care of her. This would show Astrid how much he cares, and she would likely appreciate his efforts, bringing them closer together.
Yes, he might. Hiccup is a character from 'How to Train Your Dragon' series. If there is an interesting HTTYD 2 fanfiction out there, it's possible that someone could imagine Hiccup reading or being involved in it in some way in the context of fan - created stories.
If Naruto snaps at Inari, it could also affect the morale of the group they are in. Some characters might side with Naruto, while others might think he overreacted. This division within the group can create sub - plots and more complex storylines in the fanfiction.
It can create a rift. Sakura might be hurt by Naruto's outburst and start to distance herself from him. This could lead to a period of coldness between them where they don't communicate as much.
Another way could be through the use of some unique inventions he has created. Hiccup is known for his creativity in making gadgets. He could use a device that creates a temporary shield or a flying contraption that allows him to quickly move to a location that is out of reach of his pursuers.
Naruto snapping at Team 7 can split the group. This split could lead to different story arcs for each character. Maybe Naruto goes off on his own adventure and Team 7 has to continue their mission without him. As they each face different challenges, their growth and development are affected, and this can completely change the direction of the story. Also, it can attract the attention of antagonists. If the team is in disarray because of Naruto's outburst, villains might see it as an opportunity to attack.
It can create a major turning point. If Shinji has always been submissive before, his snapping can change the power dynamic between him and Gendo. This might lead to Shinji taking more control of his own actions and decisions in the story.
It might change Naruto's character development. If he snaps at his family, he could become more independent or more reclusive. For example, he might decide to go on a solo journey to figure out his feelings, which would be a big change from his usually family - centered self in some fanfiction scenarios. This would then drive the plot in different directions.