Kakashi is very much alive in the Boruto manga. The manga doesn't include his death. Maybe you got some misinformation or confused it with another character's fate. But for sure, Kakashi is around.
Their relationship might not change much directly. Kakashi reading Jiraya novels is more of his personal interest. But Kakashi could share some interesting parts from the novels with Naruto, which might make Naruto feel closer to Kakashi as they both have a connection to Jiraya in different ways.
Well, one similarity could be their determination. In the fanfic, like in the original series, both Naruto and Kakashi are very determined. Naruto is always striving to become Hokage and Kakashi has his own goals and missions he's dedicated to. They also might share similar combat styles in the fanfic, perhaps Naruto starts to adopt some of Kakashi's strategic thinking during battles.
People write it because they see a deep connection between Kakashi and Naruto in the original series. They might feel that there's potential for a different kind of relationship that wasn't fully explored in the anime or manga. So they use fanfiction to expand on that.
In Naruto fanfic, 'Kakashi knots' can play a role in character identification. If someone is imitating Kakashi, they might try to copy his knot style. It's like a signature look.
This kind of content is often not within the realm of typical and appropriate fanfiction. Such scenarios are considered inappropriate and against the spirit of the Naruto series.
As of now, Naruto and Sasuke haven't died in the Boruto manga. Their characters continue to play significant roles and contribute to the story's development.
Sasuke could be a popular character. He might be involved in the story in a way that either helps or hinders the situation where Naruto hurts Kakashi. For example, if Sasuke tries to stop Naruto from doing something stupid that would hurt Kakashi.