Kurama is often depicted as mischievous in fanfiction. His powerful and somewhat arrogant personality leads him to play pranks on Naruto. He might think it's beneath him to be so closely tied to a human, so he uses pranks as a way to assert some sort of control or just to amuse himself.
Kurama's pride also plays a part. Since he is a great and powerful tailed beast, he may see Naruto as a bit of a naive youngster. His pranks could be a way of teaching Naruto, in a rather unorthodox way, about the power he has within him. For instance, by making Naruto's chakra do unexpected things during training, Kurama is forcing Naruto to learn how to better control it. This is like a tough - love kind of prank. In addition, Kurama's loneliness deep down might also contribute. Pranks could be his way of getting Naruto's attention and forming a more unique bond with him, even if it's through these somewhat annoying antics.
In some Naruto fanfiction, Kurama might prank Naruto by making his chakra go haywire at inconvenient times, like during a spar with Sasuke. It could be a harmless prank where Naruto's Rasengan suddenly fizzles out because Kurama messed with the chakra flow just for fun.
He might replace Sasuke's kunai with candy - shaped ones. It would be really funny when Sasuke tries to use them in a fight or training. Another prank could be that Naruto hides Sasuke's training gear and replaces it with a bunch of candies.
He might be more calm. Since the female Kurama could be a stable influence, Naruto wouldn't be as impulsive.
Naruto could be a disruptor of the status quo. In the Highschool DxD world, there are set power structures and politics. Naruto, with his straightforward and often naive view of right and wrong, would likely not abide by some of the more underhanded practices. He'd probably be a force for good, using his ninja skills and Kurama - enhanced power to protect the weak.
Yes, in certain fanfictions. Fanfic writers like to play around with established concepts. They might see Kurama's close bond with Naruto and decide to create a scenario where Kurama is Naruto's father. This can lead to really interesting and unique story developments that deviate from the normal Naruto narrative.
One of the funniest pranks could be that the Kyuubi makes Naruto's clones start singing cheesy pop songs instead of following his commands. Naruto often uses his clones in battles and for various tasks. So when he sends them to attack an enemy, they all start singing and dancing instead. This would not only be a shock to Naruto but also to his opponents. Another great prank would be the Kyuubi making Naruto's body move in the opposite direction of what he wants. So when he tries to jump forward, he jumps backward instead, leading to all sorts of comical situations.
Sakura's reactions can vary. Sometimes she tries to get revenge on Naruto for his pranks. If he plays a prank that makes her look silly in front of Sasuke, like the fake love letter prank, she'll be really mad and try to think of a way to make Naruto pay. Sasuke might pretend not to care, but if the prank affects his image too much, like the hair product switch, he'll give Naruto a cold stare. Kakashi is more laid - back and just watches the whole thing unfold like it's entertainment.
Naruto's self - confidence gets a huge boost. Kurama's teachings are like a seal of approval. If Kurama believes in him enough to teach him, then Naruto must be something special. This new - found confidence shows in his posture, his speech, and how he faces challenges. He no longer doubts himself as much when it comes to difficult tasks, whether it's a tough battle or a diplomatic negotiation within the ninja world.
It might be portrayed as a very strong and almost spiritual connection. They could be shown as two halves of a whole, with Naruto relying on Kurama not just for power but also for emotional support and vice versa.
Naruto's optimistic personality is a big factor. His ability to always see the bright side of things can rub off on Sakura. For example, if Sakura is worried about a mission, Naruto will be all like 'Don't worry, Sakura -chan! We've faced tougher things and we always come out on top!'. His positive outlook makes Sakura believe that things will be okay.