Well, Kyuubi might influence Naruto's growth by providing him with a sense of power from within. Since Kyuubi is like a mother figure, she could be a source of emotional support too. Naruto may draw strength from their connection, both in tough battles and in dealing with his own insecurities.
In this fanfiction, one unique plot point could be the way the Kyuubi's power is intertwined with Naruto's family heritage. Since the Kyuubi is now considered his mother, it might change how Naruto discovers and masters his own powers. For example, instead of seeing the Kyuubi as a force to be tamed, he could see it as an inheritance to be understood.
Naruto's character development would be drastically different. He might be more in tune with his 'fox - like' nature from the start. Instead of fearing the Kyuubi's power, he could embrace it as part of his identity.
Well, it might be that in the fanfiction, Naruto goes to the frozen waterfall to have a conversation with Kyuubi. They could be discussing Naruto's growth as a ninja and how Kyuubi's power can be better harnessed. The frozen waterfall setting adds a sense of isolation and mystery to the encounter.
Well, one reason could be that the author wants to explore an alternate universe. Maybe in this fanfiction's version of the Naruto world, the events leading to the sealing of the Kyuubi never occurred. It could be due to different political situations among the ninja villages, or perhaps a different chain of events that prevented the Kyuubi's attack on Konoha in the first place. So, without the attack, there was no need for the seal.
It could be in an alternate universe fanfic where the rules of the Naruto world are completely rewritten and Naruto's identity as the kyuubi is central to a new and unique storyline.
Yes, there are likely such fanfictions. In the Naruto universe, Naruto has a special connection to the Kyuubi. Fanfiction writers often explore unique relationships. They might imagine Naruto and Kyuubi as mates in a way that delves into their shared experiences, like Naruto's use of the Kyuubi's power and how that could be translated into a more intimate, mate - like bond in a fictional scenario.
It might be. The Kyuubi is a very important part of Naruto's story, so it's likely that many fanfiction writers would explore it. However, it's hard to say if it's a 'popular' concept without more research into the Naruto fanfiction community.
Kyuubi's comfort can make Naruto more confident. Knowing that he has Kyuubi's support, he may take on more difficult missions without hesitation. For instance, if he's facing a powerful enemy, he'll remember Kyuubi's words of encouragement and stand his ground firmly.