At first, their relationship would be full of tension. Naruto would be cautious around Fem Orochimaru as he knows her past. But as he spends time with her, he might start to notice small changes in her behavior. For example, she may start to show more respect for life. And Orochimaru, being a slave, would have to follow Naruto's commands, which could lead to her grudgingly respecting his authority.
One possible plot could be that Fem Orochimaru, for some reason like a powerful jutsu backfiring on her, is forced to become Naruto's slave. Naruto, being the kind - hearted person he is, might initially be uncomfortable with the situation but gradually tries to understand Orochimaru's past and motives. He could use this opportunity to reform her and make her use her skills for good. For example, Orochimaru's knowledge of forbidden jutsus could be used to help the village in some way.
One possible reason could be Naruto's unique power. Naruto has the Nine - Tails within him, which is an extremely powerful and mysterious force. Orochimaru, being a character always interested in power and forbidden jutsu, might be obsessed with Naruto in fanfiction because he wants to study or even obtain that power for himself. Also, Naruto's strong - willed personality and his ability to change the people around him could be fascinating to Orochimaru who has always been somewhat of an outcast in the Naruto world.
There might be some fanfictions with such a concept, but this is a rather unorthodox and not in line with the positive themes of the original Naruto series. In the original story, Kushina is Naruto's mother, and their relationship is based on family love and the greater Ninja world narrative.
In a fanfiction where Naruto becomes an Orochimaru fan, perhaps Orochimaru has a change of heart and starts to use his knowledge for the good of the village. Naruto witnesses this new side of Orochimaru and is inspired. He begins to study Orochimaru's techniques more closely, believing that he can also use them for good. However, others in the village are skeptical and Naruto has to fight to prove that Orochimaru can be a positive influence.
Yes, there are some out there. You can start by looking on popular fanfiction websites like Fanfiction.net or Archive of Our Own. Just search for 'fem Orochimaru loves Naruto' and you'll likely find a variety of stories with different takes on this rather unique concept.
It could be about Fem Orochimaru having a different relationship with Naruto. Maybe she sees him as a potential ally or apprentice in a new way compared to the original Orochimaru.
You can try searching on fanfiction websites like FanFiction.net or Archive of Our Own. Just type in 'Fem Orochimaru Naruto' in the search bar and you'll likely find some relevant fanfictions.
One possible fanfiction could involve Fem Orochimaru seeing Naruto as a unique specimen. Maybe she's intrigued by his unwavering will and the power of the Nine - Tails within him. She might try to get closer to him in order to study his power source. For example, she could disguise herself and join Naruto on some of his missions, all the while observing him secretly.
I'm not sure if it's popular. There are so many Naruto fanfictions out there that it's hard to tell which ones are popular and which ones aren't. It could be a niche idea that only a small group of fans are interested in.