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.
There may be. Fanfiction is a vast world, and the Naruto fandom is quite large. Since Kushina has a connection to the Kyuubi in the Naruto series, it's possible that fans have explored their relationship in fictional stories. However, the availability might depend on how popular this particular pairing is among the fanfic writers. Some pairings are more common and thus have more stories written about them, but it's still worth looking for.
I'm not sure specifically about 'Kushina Kyuubi Lemon' fanfiction. However, to find good fanfiction, you can start by checking popular fanfiction websites like FanFiction.net or Archive of Our Own. Search for relevant tags and read reviews from other readers to gauge the quality.
It could be Orochimaru. He might have manipulated Kushina into kidnapping Naruto. Orochimaru has always been interested in the power of the Uzumaki clan and Naruto's nine - tailed fox power. He could be using Kushina as a tool to get to Naruto.
Maybe in the fanfiction, Kushina kidnaps Naruto because she believes she can protect him better away from the Hidden Leaf Village. She thinks the village has become too dangerous for him. However, Naruto doesn't understand her intentions at first and struggles against her. As the story progresses, he realizes her love and the real reason behind her actions.
Another aspect could be that the Kyuubi is being controlled by a hidden force when it kidnaps Naruto. This hidden force might be using the Kyuubi's power to start a war between the village and other hidden villages. They could be framing the Kyuubi to create chaos, and Naruto, being the jinchuriki, is the key piece in their evil plan. Naruto might then have to figure out a way to break free from the Kyuubi's hold and expose the real villains behind the kidnapping.
Naruto might initially be shocked and angry. He has always considered the Kyuubi as an enemy within him, and now being kidnapped by it is the worst - case scenario for him. He could try to fight back immediately, using whatever little chakra he can muster without relying on the Kyuubi's power.
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.
Common themes may include the power dynamics between Kyuubi and Kushina. Since Kyuubi is a powerful entity and Kushina was its host, fanfiction might play with this idea in various ways. In some lemon fanfiction, there could be themes of forbidden love or a complex relationship that goes beyond the normal host - tailed beast relationship. But again, due to the 'lemon' nature, these stories can be quite adult - oriented and not for everyone.
The unique aspect could be the combination of Kushina and Kyuubi. Kushina has her own backstory and character traits, and when paired with the powerful and mysterious Kyuubi in fanfiction, it can create some really interesting storylines. It might explore different relationships or scenarios that are not seen in the original source material.