His relationships would become more complex. The villagers who once hated him for having the Kyuubi inside him might now be even more terrified as he has its soul. However, Naruto's friends like Shikamaru would likely see this as an opportunity for Naruto to grow even stronger. They would try to help him harness this new power while also making sure he doesn't lose himself to the Kyuubi's wild nature. This new situation would test all of his relationships.
He might gain enhanced chakra control. Since he has the Kyuubi's soul, he could have better access to the Kyuubi's chakra reserves and be able to manipulate it more precisely. Maybe he could also gain some of the Kyuubi's natural abilities like better senses, especially smell, which could help him in tracking enemies or finding things.
Well, in some versions of 'naruto gets kyuubi soul fanfiction', Naruto may have to deal with the Kyuubi's memories. These memories could be of battles long ago or the Kyuubi's past experiences. This could lead to Naruto having a deeper understanding of the world of chakra and the history of the tailed beasts. Also, there might be a plot where Naruto has to convince the Kyuubi soul to fully cooperate with him, rather than just being a power source.
Naruto becomes more confident. With the Kyuubi soul, he has a new source of power that makes him feel like he can take on bigger challenges. For instance, he might be more assertive in battles and negotiations.
Yes, in some fanfictions, Naruto is often depicted as the Kyuubi or having a very close connection to it. This can lead to really interesting and unique storylines that deviate from the original plot.
One common plotline is the Kyuubi teaching Naruto new and powerful jutsu. Since the Kyuubi has a vast amount of chakra and knowledge, it could share unique techniques with Naruto that are not part of the regular ninja training. Another plotline could be the Kyuubi's influence on Naruto's relationships. For example, some fanfictions explore how Naruto's connection with the Kyuubi affects how his friends and villagers perceive him. It can also lead to some interesting character development as Naruto has to learn to control the Kyuubi's power without being consumed by it.
In many Naruto fanfictions, Naruto might have developed some new and unique abilities that the Kyuubi has no defense against. This could make the Kyuubi, which is used to being a dominant and feared force, feel vulnerable. For example, if Naruto has the power to nullify the Kyuubi's chakra or to manipulate it in a way that goes against the Kyuubi's will, it would be a cause for fear.
In some fanfictions, when Naruto has the Kyuubi extracted, he often becomes extremely weak. His life force is severely depleted as the Kyuubi was a major source of his power. He may also face psychological trauma from losing such a huge part of himself that had been with him since birth.
Maybe it's because Naruto has some sort of special connection or resemblance to the Kyuubi that Kushina notices. For example, Naruto might display some of the Kyuubi's power characteristics in an obvious way that makes Kushina jump to that conclusion.
At first, Naruto might see the Kyuubi as just a source of power. But as he starts to protect it, he realizes it's more of a partner. Their relationship evolves from a simple user - power source dynamic to a deep - seated friendship. He begins to understand the Kyuubi's emotions and past, which further cements their bond.