No, it's not appropriate. Naruto is a story that promotes values like friendship, hard work, and loyalty. Fanfiction with themes of cheating goes against these values and can also create a negative view of the characters. Moreover, 'lemon' often implies sexual content which is not suitable for a general audience.
There could be. Since Naruto has a large fan base, fans create all kinds of fanfictions. However, it might not be a very common or popular theme as Mei Terumi doesn't have a very direct romantic connection with Naruto in the original series. But it's still possible that some creative fan has come up with such a plot for the sake of exploring different relationships and scenarios in the Naruto universe.
One common theme is the breakdown of relationships. For example, when a character cheats, it shatters the trust between them and their partner. Another theme is the exploration of the darker side of characters. In the original Naruto series, most characters are portrayed as noble, but in these fanfictions, their actions can be much more morally ambiguous.
I'm not sure if there is such specific fanfiction. Fanfiction can cover a wide range of wild and unexpected scenarios, but this one seems rather unethical considering the original relationships in the Naruto series. It's also not in line with the positive and loyal characters' personalities in the original work.
One common theme is broken trust. Since it's about 'cheating', characters often find out that someone they trusted has been lying or acting against their interests. Another theme is the fall - out from such actions. How Naruto or other characters deal with the disappointment and anger that comes with being cheated.
Well, there might be some very niche or non - canon fanfictions out there with such a plot, but it's not a common or widely - accepted idea in the Naruto fan community. Naruto and Hinata have a well - established relationship in the main series, and Neji is Hinata's cousin, which makes such a relationship in the context of cheating even more inappropriate and not in line with the general themes of the series.
One possible reason could be a miscommunication between them. Maybe Anko feels neglected and then strays. Another reason might be that the writer wants to create a more complex and angsty plot.
Naruto might be initially heartbroken. He is a character who values loyalty and love deeply. So, when he discovers Hinata's cheating, he could be in a state of shock and disbelief.
However, Naruto is also a very loyal and understanding person deep down. So after the initial shock and anger, he would probably start to investigate the situation more. He might talk to their friends like Shikamaru or Sakura to see if they know anything. He would want to get to the bottom of it rather than just making a hasty judgment.