A common theme is adaptation. Naruto has to adapt to the new rules and society in the Highschool DxD world. There are also themes related to good vs evil. In both universes, there are forces of good and bad, and in the fanfic, these forces often clash or cooperate in new ways. For example, Naruto might team up with the devils to fight a greater evil.
One main theme is power. Since both Naruto and Highschool DxD have characters with different levels of power, in the fanfic, it's often about how Naruto's power compares and combines with the powers in the DxD world. Another theme is friendship. Naruto is all about friendship, and in the DxD world, there are also relationships to be formed and maintained.
Another theme is the origin of ninja techniques. Fanfics might focus on how the First Hokage developed his signature jutsu, like his powerful wood - style techniques. They might also explore how he passed on his knowledge or if there were any secrets behind his abilities. This can add a lot of depth to the story as it ties in with the overall Naruto universe's focus on jutsu development.
One common theme is the combination of different elemental powers. Since Naruto has his own set of abilities related to chakra and Korra is an Avatar with control over four elements, fanfics often explore how these powers can work together or create new forms of combat.
Identity is also a big theme. Since the fox transformation is such a big part of Naruto, fanfics will look at how this transformation affects who he is, whether he's seen as more of a monster or a hero because of it. For example, in some fanfics, his friends have to come to terms with this new, more powerful and somewhat wild - looking Naruto. And it really makes for an interesting exploration of relationships as well.
One of the main themes is the clash of different power systems. Since Fate Stay Night has its own magic system and DxD has its devil powers and sacred gears, fanfictions often explore how these powers interact when the two universes collide. For example, how would a mage from Fate Stay Night fare against a high - level devil in DxD? Another theme is the relationships between characters. There could be new friendships or rivalries formed between characters from the two different series. It's interesting to see how, say, a character from Fate Stay Night might view the rather unique social structure in the DxD world.
Power and self - discovery are also frequently explored. Shihoin may start out with certain abilities but then uncovers new powers or aspects of themselves as the story progresses. For example, in some fanfictions, Shihoin has to learn to control a new and powerful jutsu. This theme ties in with the overall theme of growth that is prevalent in the Naruto series.
One common theme is the clash of cultures. Since Naruto's world has its own set of values, ninja clans, and a unique power system, and Highlander has its own lore about immortals and their rules. When combined, it often leads to exploring how these different cultures interact and adapt to each other.
Power and its limits. When Naruto characters enter the Fate universe or vice versa, they have to figure out how their powers stack up. For instance, Naruto's huge chakra reserves compared to the magic in Fate Stay Night.
Another common theme is self - discovery. They might each go through a journey of finding out more about themselves while also being there for their friend. For example, Maxxie might be exploring his identity in the world of fashion and dance, and Anwar could be on a path of finding his own voice in different areas like music or academics, all while relying on their friendship as a support system.
One of the themes is teamwork. Since they are often associated with group activities, fanfics may explore how they work together effectively. Also, loyalty is a theme that is frequently seen, showing their loyalty towards each other in different scenarios which can be really heartwarming.
Naruto would probably be very friendly and curious. He'd be excited to meet all the different types of beings in the Highschool DxD world. He might start by trying to make friends with Issei, sharing his stories about his own battles and adventures in his world.