Often, there is a trope of the Kyuubi being possessive in a motherly sense. It doesn't like other people or things that might harm Naruto. So it would be very wary of any new threats or characters that come too close to Naruto. And sometimes, there's a trope of Naruto and the Kyuubi having a kind of mother - son telepathic connection, where they can communicate their feelings and thoughts without speaking.
A frequent trope is the emotional bond between them. Naruto might seek comfort from the Kyuubi during tough times, and the Kyuubi would be there for him. There could also be a trope where Naruto tries to make the Kyuubi proud, similar to a child trying to impress their mother. He would constantly strive to become stronger and better at using the Kyuubi's power in a positive way.
In such fanfictions, the relationship between Naruto and Kyuubi can be developed in various ways. For example, the Kyuubi could start teaching Naruto about his heritage in a more motherly way, like sharing stories of the Uzumaki clan. Naruto, on the other hand, could show his loyalty and love towards the Kyuubi as he would to a mother. This could also impact his relationships with other characters. His friends might be initially confused but later come to understand and support this new relationship of Naruto's.
One interesting 'Naruto Kyuubi Mother' fanfiction could be where the Kyuubi's mother has a backstory of being a powerful spirit from an ancient era. In the fanfic, she might be trying to protect Naruto from afar, using her hidden powers to influence his growth and development.
One common trope is the 'Forbidden Love' between Naruto and the female Kyuubi. Since she is a powerful and somewhat dangerous being, their relationship is often seen as something that goes against the norms of the ninja world. Another trope is the 'Power - Up' trope, where Naruto gains new and stronger abilities through his connection with the female Kyuubi.
Often, in these fanfictions, Naruto has a hidden power that is related to his Uzumaki heritage. This power awakens when he realizes Kushina is in danger from the Kyuubi. He then uses this power to not only save Kushina but also to tame the Kyuubi in a way that no one has ever done before. It could also be that Naruto has made a deal with some other powerful entity that gives him the means to save Kushina from the Kyuubi.
One popular trope is the 'Powerful Protector'. Naruto, with his Kyuubi powers, is always there to protect Hinata. For instance, when a group of rogue ninjas attacks the village, Naruto's Kyuubi - enhanced strength and speed allow him to quickly come to Hinata's rescue. It's a classic trope that shows his devotion to her.
One common theme is family. Since Kushina is Naruto's mother, fanfictions often explore the family bonds. They might show how Naruto's connection to Kushina affects his relationship with the Kyuubi. Another theme is power. The Kyuubi's power within Naruto is a huge aspect. Fanfictions may deal with how Naruto learns to control it, and how Kushina's own experiences with the Kyuubi's power can help or hinder Naruto. Redemption can also be a theme. The Kyuubi, which was once seen as a monster, could be redeemed through its relationship with Naruto and the influence of Kushina's memory.
Some common themes are power and its control. Since Kyuubi is a very powerful entity, fanfictions might explore how Naruto learns to control the power she gives him in a more nuanced way. Family and acceptance is also a big theme. Naruto, who grew up without parents, now has this 'mother' in Kyuubi. Fanfictions could show how he comes to terms with this new form of family. Additionally, the protection theme is there. Kyuubi, as Naruto's 'mother', would naturally want to protect him, and this can lead to many interesting plotlines where she defends Naruto from various threats.
One popular trope is the 'power - up' trope. Writers often have Naruto gain new and enhanced abilities while in his Kyuubi fox form. For example, he might be able to fly or have enhanced speed and strength that far exceed his normal capabilities.
One common theme is power growth. Naruto's development of new skills under the fem Kyuubi's training is often explored. Another is the relationship aspect, like whether they become friends or something more. And there's also the theme of self - discovery for Naruto as he learns more about himself through the training.
A frequent theme is the struggle between good and evil. Dark Naruto represents a darker side, and the Female Kyuubi can be seen as either a force for good or bad depending on how the story is written. Their relationship also often explores themes of trust and betrayal as they try to figure out if they can rely on each other.