Well, in such fanfictions, Naruto often relies on his ninja skills, along with the support of his friends and mentors. Sometimes, he also taps into hidden reserves of chakra and unlocks special abilities to battle the Kyuubi.
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.
Well, Naruto could save Kushina from the Kyuubi in fanfiction through his strong willpower. We know Naruto has an unbreakable spirit. He might be able to communicate with the Kyuubi in a different way, like showing the Kyuubi a future where it doesn't have to be so violent. And by doing this, he could convince the Kyuubi to release Kushina. Also, Naruto might have received some special power or training that enables him to counter the Kyuubi's attack and save Kushina.
On the positive side, some might see Naruto as a powerful asset. Since the Kyuubi is extremely powerful, if they believe Naruto is the Kyuubi, they could try to use his power for their own good. However, this also means they might not see Naruto as an individual with his own feelings and will. His relationships would become more about what he can do for others rather than true friendship.
One possible consequence could be chaos in the ninja world. With Naruto, a major force for peace, dead and the Kyuubi released, other villages might see an opportunity to gain power or territory. Villages that once relied on Naruto's protection would be vulnerable. Also, the Kyuubi, being a powerful and wild force, could start causing destruction on its own, without Naruto to control it.
One common way is through power boosts. The Kyuubi's chakra gives Naruto the strength to take on tougher opponents.
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 some fanfictions, Naruto might obtain the Kyuubi's bloodline through a special ritual. This could be a ceremony performed by a powerful shinobi or a sage who has the knowledge to transfer the essence of the Kyuubi's power into Naruto's genetic makeup, thus giving him the bloodline.
Well, in some fanfictions, Naruto might obtain the sword through a special bond or trial. Maybe Kyuubi decides that Naruto needs this weapon to face a new and powerful enemy. So it could be that Naruto proves his worth in some way, like showing great courage or a new level of control over his chakra, and as a result, Kyuubi gives him the sword.
Perhaps Naruto feels that Kushina is being overprotective. He wants to prove his independence and go on his own adventures without her constant supervision, so he decides to run away.
It could mean control. Maybe the fem Kyuubi has the ability to influence Naruto's actions or decisions in the fanfiction.