Sesshomaru would likely be aloof and haughty at first. He might look down on Naruto as a mere human. Naruto, being his friendly self, would probably be curious about Sesshomaru and try to start a conversation. Sesshomaru might respond with cold remarks, but Naruto's persistence could gradually break through his icy exterior.
One possible plot could be that Sesshomaru, while traveling through different dimensions, ends up in the Naruto world. He might initially be seen as a threat and have to fight some of the ninja. But then, he could encounter Naruto, who is curious about him instead of being hostile. They could team up to fight a common enemy, like an Akatsuki member who has a new, powerful jutsu that could endanger both their worlds.
One possibility could be that Kagome is initially afraid of the younger Sesshomaru. In the fanfiction, she might mistake his youth for weakness at first, but soon realizes that he still has his pride and power. This could lead to an interesting dynamic where she has to re - evaluate her preconceived notions.
There are definitely some out there. I've seen ones where Naruto is put in a situation similar to Sesshomaru's, like having to deal with a powerful enemy or a complex moral dilemma in a way that Sesshomaru might. It's really interesting to see how authors blend the two very different universes of Naruto and Inuyasha (where Sesshomaru is from).
There probably is. Fanfiction writers often come up with very creative and unexpected crossovers. However, the quality can vary greatly. Some might be really well - written with interesting plotlines that blend the Naruto and Inuyasha universes in a unique way considering the relationship you mentioned, while others might not be as good.
One possibility could be that in this fanfiction, female Sesshomaru uses her demon powers to protect Naruto. Maybe she has her own motives, like she sees a kind of potential in Naruto similar to what she once saw in someone else. She could be a very strict but effective guardian, teaching Naruto new combat techniques from her own demon - related knowledge.
Well, Kagome could end up helping younger Sesshomaru when he is injured. This would be a big shift in their relationship as Sesshomaru is not one to usually accept help from a human. But since he is younger, he might be more vulnerable and thus more likely to accept her aid.
Obviously, Kagome and Sesshomaru's pups are the main characters. Kagome, the modern - day girl who got transported to the feudal era, and the pups, who are part of Sesshomaru's lineage.
In this fanfiction, it could be that the pups are in some sort of danger, like being hunted by a powerful demon. Kagome, with her spiritual powers and knowledge from her own world, steps in to save them. As she spends time with the pups, she starts to understand more about Sesshomaru through them. Maybe the pups are also curious about Kagome and her different scent and appearance. This encounter could also be a way to bridge the gap between Kagome's group and Sesshomaru, leading to new alliances or at least a truce in the ongoing battles in the feudal era.