One possible reason could be Naruto's natural sense of justice. He can't stand to see a child in danger, and Koyuki being a child at that time, Naruto's heroic nature kicks in. He has always been the type to help those in need.
One idea could be that they use their combined powers to protect the Hidden Snow Village from a new and powerful enemy. Naruto's godlike abilities, like his massive chakra reserves and his sage mode skills, along with Koyuki's leadership and knowledge of her village, make them a formidable couple.
Yes, there are quite a few. You can start by looking on popular fanfiction websites like FanFiction.net or Archive of Our Own. Just search for 'naruto and koyuki romance' and you'll find a variety of stories with different plotlines and writing styles.
Another type of Naruto Koyuki fanfiction might be a story where Koyuki discovers a new power within herself with Naruto's help. Maybe she has some latent ice - related abilities that are unlocked when Naruto accidentally stumbles upon a hidden scroll in her village that reveals the secrets of her family's bloodline limit.
There might be. A lot of fanfiction writers are creative and might have explored the idea of Naruto and Koyuki getting married. However, the quality can vary greatly. Some might focus more on the romantic aspect, while others could incorporate more action and adventure elements into the story of their married life.
One common theme is friendship. Since Naruto is known for his ability to befriend others, in fanfics with Koyuki, their friendship often plays a crucial role. Another theme could be adventure, as they might go on quests together.
One great Naruto and Koyuki fanfiction could be 'Naruto's Winter Adventure with Koyuki'. It might explore their relationship in a new adventure set in a snowy landscape. Another could be 'Koyuki and Naruto: Bonds Beyond the Screen' which delves into how their bond develops in a unique way not shown in the original series.
Megumi Kato is a character in the light novel. She often has certain characteristics and a role to play within the story of the light novel. However, without more specific information about which particular light novel she is from, it's hard to go into great detail about her.
I'm not familiar with the 'King Kato story'. It might be a unique narrative perhaps about a king named Kato who had his own adventures, ruled a kingdom, and had various experiences like dealing with political intrigues, wars, or building his kingdom. Without more information, it's hard to say exactly what the story is.