Another aspect of the training could be mental discipline. Hayate may introduce Naruto to meditation - like techniques to help him focus his chakra more effectively. He'd also likely teach Naruto how to keep a calm head in the heat of battle, sharing his own experiences to illustrate the importance of mental fortitude.
Physically, Naruto could become more proficient in close - quarter combat. His reflexes might improve significantly, allowing him to dodge attacks more easily. His overall strength and endurance could also increase as Hayate likely has a strict training regime.
Well, in many fanfictions, Naruto might use his chakra to heal Hayate. Since Naruto has a large amount of chakra and has learned some healing techniques over time, he could transfer his chakra into Hayate's body to repair the damaged parts.
Another problem might be the lack of proper resources. Even if Naruto has the ability to heal, he may not have all the necessary herbs or medical equipment. In the world of Naruto, some healing requires specific items. If they are in a remote location or in a battle - torn area, getting these resources could be a huge hurdle.
Kosuke might be a character created specifically for this fanfic. He could be someone with a unique background, like perhaps he was once a disciple of a great ninja but then went on his own path. And now he sees potential in Naruto and decides to train him. He could have abilities that are different from the main characters in the original Naruto series, which is why he has something new to offer to Naruto in terms of training.
In this fanfic, Lilith could be an original character created by the author. She might be a powerful and mysterious figure with special abilities that make her suitable to train Naruto.
She could be someone with a special bloodline or ability. Maybe she has a unique form of chakra that gives her certain powers. In the context of training Naruto, her skills and knowledge are what make her important. She could be a mysterious figure who has been observing Naruto for a while and decides to take him under her wing to help him reach his full potential. For instance, she might have the ability to see the latent potential in others and wants to shape Naruto into a great ninja not just for his own sake, but also for the greater good of the ninja world.
It could lead to Naruto becoming even stronger and more skilled than in the original story. Jiraiya's training methods might unlock new powers for him.