In fanfiction, Naruto in his Kyuubi form could have a more solemn personality. The power of the Kyuubi might make him more aware of the weight of his responsibilities. He could become more of a brooding figure, constantly thinking about how to use his power for the greater good and not let it get out of control.
In some fanfics, when in Kyuubi form, Naruto can be more aggressive. The Kyuubi's influence might make him less hesitant in battle and more direct in his attacks.
In some fanfictions, the Kyuubi's power could be depicted as more spiritual. Instead of just raw chakra, it could have elements of ancient wisdom and spiritual energy that Naruto can tap into. For example, Naruto might be able to use the Kyuubi's power to communicate with the spirits of the past. Another way is to show the Kyuubi's power as having different forms. Maybe there's a 'benevolent' form of the Kyuubi's power that Naruto can access for healing or peace - making purposes, as opposed to the more destructive form we usually see.
In terms of relationships, fem Naruto could have a more complex relationship with Sasuke. Maybe she doesn't have the same kind of one - sided crush as Naruto did in the original. Instead, they could start as rivals but slowly develop a mutual respect and understanding that is based on their shared experiences and growth as ninjas.
Nagato, in fanfiction, can be depicted in various ways. Some may show him as a more conflicted character. He has his own beliefs which were shaped by his experiences, like the death of his friends and the destruction he witnessed. He may be more hesitant to change compared to Naruto, but also has the potential for redemption which makes his character interesting.
Well, a lot of fanfictions play around with the appearance of the Sage Cloak. They might make it look more elaborate or even give it new markings. This not only makes Naruto look more badass but also can symbolize new levels of power or a connection to different aspects of the Sage Mode. Some fanfictions also change how the cloak is summoned, like it could be summoned instantly without the need for Naruto to gather chakra in the traditional way.
In some fanfiction, their friendship might be more openly affectionate. In the original series, they were a bit more reserved. But in fanfic, they could be shown hugging or being more verbally expressive about their feelings for each other. For example, Naruto might say more heartfelt things to Sasuke about how much he values their friendship.
In some fanfictions, Shisui's Sharingan has a different color or pattern. This is a simple but effective way to make it stand out. For example, it could be a deeper red or have an extra swirl in the pattern.
Often, Kyuubi's protectiveness is shown through its internal dialogue or actions. For example, it might mentally warn Naruto about a character who seems untrustworthy in a yaoi relationship. Or it could physically manifest some of its power to intimidate others who might harm Naruto.
Often, she's portrayed as having a complex relationship. Some fanfictions show that her sealing of the Kyuubi was not just a physical act but also left a spiritual mark. So, the Kyuubi might be more docile towards Naruto because of its past with Kushina.
Their relationship could be portrayed as a mentor - mentee relationship in a different way. Instead of Orochimaru trying to use Naruto for his own gain, he could genuinely see Naruto's potential and guide him in the ways of some of the more esoteric jutsu. For example, Orochimaru could teach Naruto about the secrets of the snake contract without any ulterior motives. Another way is to show them as reluctant allies. Maybe there's a common enemy that is so powerful that they have no choice but to work together, and over time, they start to respect each other's abilities.