The idea of self - discovery is often explored. Fem Harry, being in a new and different world like Naruto's, has to figure out who she is outside of the context of the Harry Potter universe. This can involve her learning new skills, understanding new cultures, and finding new strengths within herself.
One interesting crossover could be the magic system of Harry Potter combined with the ninja skills in Naruto. For example, a story where Naruto characters learn to use wands and spells while Hogwarts students learn chakra control. Another could be a plot where Voldemort teams up with Orochimaru to take over both the wizarding world and the ninja world. There could also be a story about Harry Potter being reincarnated as a ninja in the Naruto world and using his knowledge of magic in new and unexpected ways.
One popular pairing is Naruto and Hermione. The idea of Naruto's energetic and somewhat naive nature paired with Hermione's intelligence and studiousness can create an interesting dynamic. Naruto might be in awe of Hermione's knowledge, and Hermione could be intrigued by Naruto's unique abilities.
One interesting crossover could be the use of ninjutsu in the wizarding world. For example, Naruto's shadow clone jutsu could be used by a Hogwarts student to attend multiple classes at once, leading to all sorts of comical and chaotic situations in the hallways of Hogwarts.
Another theme is friendship or sometimes even romance. Since it's Naruto and fem Harry Potter, the stories often explore how two very different characters from different universes can form a deep connection. They support each other in battles against common foes and also in understanding their respective worlds better.
One common theme is the clash and combination of different powers. Harry has magic from the wizarding world and Naruto has chakra - based ninja abilities. Another theme is the exploration of different cultures. The wizarding culture of Harry Potter and the ninja culture of Naruto are quite distinct. And of course, the yaoi theme focuses on the romantic relationship between male characters from the two series.
Harry and Naruto are often paired as they are both the main protagonists in their stories and share the 'chosen one' archetype. Hermione and Sakura are also popularly paired, as they are both intelligent and strong female characters. Another common pairing is Ron and Choji, perhaps because they both have a bit of a comical side and are loyal friends. Also, Dumbledore and the Third Hokage could be paired in some fanfics, as they are both wise leaders in their worlds.
I'm not entirely sure if there is a specific one with that exact premise. However, fanfiction authors are constantly coming up with new and unique concepts. Given the popularity of both Harry Potter and Naruto, it's possible that someone has written a story where Harry Potter is a blacksmith within the context of a Naruto fanfiction. It could be an interesting take on the characters and their worlds, perhaps exploring how Harry's skills as a blacksmith could interact with the ninja world of Naruto.
No, it isn't. The 'harem' idea, which implies a male character having multiple romantic or sexual relationships, and 'lemon' (which often refers to sexual content) don't really fit with the general tone and values of the Harry Potter world. The Harry Potter fanfiction community mostly focuses on things like exploring new magical adventures, developing character backstories that are in line with the original, or reimagining relationships in a more platonic or canon - friendly way.
Yes, there are quite a few. You can start by looking on popular fanfic websites like Archive of Our Own (AO3). Some fanfics might focus on a crossover adventure where the magic of Harry Potter's world combines with the ninja skills of Naruto, especially with a female Naruto character. For example, there could be a story where she attends Hogwarts and has to navigate both the wizarding world's challenges and her own ninja abilities.