It could be that he's being deprived of food as a form of punishment or neglect. There might be some characters in the fanfiction who are deliberately keeping food from him, either out of spite or because they don't care about his well - being.
One possible reason could be poverty. If he doesn't have enough money to buy proper food, he'll end up malnourished. In the Naruto world, there are likely areas where food is scarce or expensive.
One possible plotline could be Naruto's struggle to keep up in his ninja training due to malnourishment. His body might not be as strong as his peers', so he has to find ways to overcome this, like secretly foraging for food or relying on the kindness of some villagers who see his plight. Another could be that his malnourishment is a result of being ostracized, and as he tries to improve his situation, he also starts to question the village's treatment of him.
One possible plot could be that Bella's malnourishment is due to a difficult situation at home. Maybe her family is poor and can't afford enough food. Her friends in the fanfiction world then notice her frail state and start to help her by bringing her food and getting her proper medical attention.
Well, it would likely slow down his progress. Malnourishment means his body doesn't have the proper nutrients to build muscle or increase stamina. In ninja training that involves a lot of running, jumping, and fighting, Naruto would get tired easily. He might not be able to keep up with his peers in sparring sessions or obstacle courses.
One possible storyline could be Peter Parker's struggle to keep his identity as Spider - Man a secret while dealing with malnourishment. Maybe he's so focused on fighting crime that he forgets to take care of himself. Another could be that due to some financial difficulties, he can't afford proper food, and this affects his performance as Spider - Man. For example, he might be slower or less able to focus during battles.
His malnourishment could make his friends worry more about him. For example, Sakura might start to be more motherly towards Naruto, constantly trying to get him to eat proper meals. His relationship with Sasuke could also change as Sasuke might initially look down on Naruto for being weak because of the malnourishment, but then as he sees Naruto's determination to overcome it, he gains a new respect for him.
It could be due to a new jutsu he's trying to master that has some side effects on his emotions. Maybe it's a powerful ice - based jutsu that's making him cold in nature as well.
Her best friend could be the first one to help. They might notice the signs of malnourishment like her pale skin and lack of energy. They start by sharing their lunches with her at school.
One story could be about a little girl in a poverty - stricken area. She is malnourished and often feels weak. Her family tries their best but lacks resources. However, a local aid group discovers her situation and starts providing proper food and medical help. Eventually, she begins to regain her strength and shows a big smile again.
It could be due to a personal loss that has hit him really hard. Maybe he lost someone very close to him, like Jiraiya all over again, but this time it has broken him in a way that he shuts everyone out. He might also be under the influence of a new power that he doesn't fully understand yet, and this power is affecting his emotions, making him cold as a side - effect until he learns to control it.
Maybe in the fanfiction, there were some political motives. Hiruzen might have been pressured by other hidden villages. They could have threatened Konoha if Naruto, as the Nine - Tails' jinchuriki, remained in the village. So, to avoid a potential war or conflict, Hiruzen made the difficult decision to banish Naruto. Also, it could be due to a misunderstanding. Naruto might have been in the wrong place at the wrong time during an incident, and Hiruzen misjudged the situation.