One possible storyline could be that Naruto, upon accepting the Kyuubi, gains new powers and uses them to protect the village in a more efficient way. He might be able to control the Kyuubi's chakra better and combine it with his own jutsu for stronger attacks.
The Akatsuki could still be the main antagonists. Even though Naruto has accepted the Kyuubi, they might see his new power as a greater threat or a valuable asset to capture. They could try to take the Kyuubi from Naruto to use for their own evil purposes.
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.
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.
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.
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.
Sasuke is often a popular character in these fanfictions. His relationship with Naruto can be further explored in the context of the Kyuubi's fatherly influence. Maybe Sasuke is initially skeptical of this new - found bond between Naruto and the Kyuubi but later comes to accept it. Sakura is also a common character. She might notice the changes in Naruto due to the Kyuubi's fatherly presence and be either supportive or a bit jealous. Kakashi could also be there. He might be observing Naruto's growth under the Kyuubi's guidance and offer his own wisdom as Naruto's former teacher.
In this fanfiction, their relationship becomes more of a partnership. Instead of Naruto just using the Kyuubi's power, they work together as brothers. Naruto might start to understand the Kyuubi's feelings and motives better.
One consequence could be that he becomes extremely powerful. His physical abilities like strength, speed, and endurance are enhanced. He can also use more powerful jutsus with the extra chakra boost from the Kyuubi.