Kawaki makes his appearance in Boruto manga at a specific point, but I can't recall exactly. You might want to check the official manga sources for the precise chapter.
It could also be related to a prophecy or a pre - determined fate in the fanfic's plot. There might be some kind of dark prophecy that says Kawaki has to kill Naruto to prevent a greater evil. Or perhaps Kawaki is being controlled by an external force that has a vendetta against Naruto and uses Kawaki as a tool to carry out the murder.
One common theme is friendship. Writers often explore how Himawari and Kawaki, who come from different backgrounds, form a bond of friendship. Another theme is growth. They both grow as characters, learning from each other.
Yes, there are many. Some fanfics might focus on their growing relationship, like how they gradually understand and support each other. For example, in one fanfic, Kawaki and Himawari start as classmates who don't get along at first. But as they face challenges together in the ninja academy, they begin to respect and care for one another.
In this kind of fanfiction, Naruto might teach Kawaki about the values of the Hidden Leaf Village. Maybe he'd show Kawaki how to control his powers better. For example, Naruto could take Kawaki on training sessions similar to the ones he had with Jiraiya.
No, Boruto is alive in the manga. The plot hasn't led to his death. However, the manga is ongoing, and anything could happen in the later developments.
One great Himawari and Kawaki fanfiction is 'The Bond of New Beginnings'. It focuses on how they start to form an unexpected friendship in the village, with Himawari's kindness breaking through Kawaki's tough exterior.