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.
One possible plot could be that Naruto grows up with a unique connection to the fem Kyuubi. Since his mother Kushina was also linked to the Kyuubi, Naruto might have an even stronger bond. He could learn special jutsus from the fem Kyuubi's chakra, which makes him stand out among his peers in the ninja academy. His relationship with the fem Kyuubi could be like a mentorship, guiding him on his path to become a great ninja.
A plotline could be that Naruto has to keep his true parentage a secret for a long time. This secrecy adds to his internal conflict as he tries to fit in with the other ninjas. As the son of Kyuubi and Kushina, he may be hunted by certain groups who want to either use his power or destroy it. He then has to go on a quest to find out more about his parents and his own identity, all while fending off these threats.
His development could be quite different. Since he has this special connection to the fem Kyuubi and is Kushina's son, he might grow up with a more refined sense of chakra control. This would make his training easier and he could progress faster in his ninja skills. Also, his attitude towards his enemies might be more understanding, as the fem Kyuubi could have taught him about the reasons behind people's actions. He could become a more diplomatic ninja, trying to find peaceful solutions first instead of just jumping into battle.
Well, in fanfictions about Naruto, Kushina and Kyuubi, their relationships can vary greatly. Some fanfictions might focus on how Naruto inherits not only the Kyuubi's power but also some of Kushina's traits. For example, Kushina was known for her strong will, and Naruto might be shown to have an even stronger will because of her influence and the presence of the Kyuubi. The Kyuubi could be portrayed as a protector of Naruto in a sense, especially when it comes to threats that are related to Naruto's family history. And Kushina could be like a spiritual guide for Naruto when it comes to dealing with the Kyuubi's power.
In fanfiction, absolutely. Fanfiction writers often like to play around with the established concepts of a story. They might create a scenario where Naruto is the son of the Kyuubi to add a new layer of mystery, drama, or just to show a different side of Naruto's character. This could lead to some really unique story arcs that deviate from the original story's family structure.
His training would likely be more intense. Since he has the blood of Kyuubi, he might have a natural affinity for chakra control and large amounts of chakra. So, his training could focus on refining and mastering this huge chakra reserve from an early age. For example, he could be taught advanced chakra - based jutsu much earlier than in the original story.
In a fanfiction like this, Fem Kyuubi's love for Naruto could be a deep, almost possessive kind of love. Since Naruto has always been different from others in how he treats the Kyuubi. As for hating Kushina, it could be that Fem Kyuubi blames Kushina for separating her from the world for so long. And this could lead to a lot of internal conflict within Naruto, who loves his mother but also has a bond with Fem Kyuubi.
One implication could be a different power dynamic. Naruto would have an even stronger connection to the Kyuubi's power. He might also face different kinds of discrimination or fear from the villagers as being related to the Kyuubi.
In some fanfictions, yes. Fanfic writers like to explore unique and out - of - the - box ideas. They might create a story where Naruto has a special connection to the Kyuubi that goes beyond just being a Jinchuuriki and make him the Kyuubi's son. It's a creative twist on the original Naruto story.