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.
Yes, he might. Kakashi is a complex character with diverse interests. Given his love for reading in general, it's not a stretch to think he could pick up a romance novel from time to time. He seems like the type who would be open to different genres to expand his knowledge and understanding of various emotions and relationships.
Their relationship is like a mentor - mentee bond. Kakashi has trained Naruto, and when he sees Naruto achieve great things, it can be overwhelming. For example, when Naruto masters a new jutsu that Kakashi thought was difficult for him, Kakashi might cry out of joy for Naruto's accomplishment.
It could become strained. Naruto snapping at Kakashi would create an initial rift between them. Kakashi might be taken aback by Naruto's outburst and Naruto, after snapping, might feel a bit guilty but also stubborn about his feelings, which would make the relationship tense for a while.
Well, Kakashi could train Naruto in combat skills specific to ANBU missions. This would include more lethal and precise attacks. He might also teach Naruto how to use different types of weapons that are common in ANBU operations. Maybe Kakashi would set up mock battles where Naruto has to face multiple opponents at once, just like in real ANBU scenarios.
Well, it could be that Kakashi, being a character who values the integrity of the original Naruto narrative, sees fanfiction as a deviation. Fanfiction might include out - of - character scenarios for him or the other characters. He might also dislike the fact that some fanfictions can be of very poor quality in terms of writing and plot, which could be a reason for his dislike.
In fanfiction, Kakashi might comfort Naruto by simply being there for him. Just sitting in silence, showing Naruto he's not alone. For example, they could be on the Hokage Rock and Kakashi would put a hand on Naruto's shoulder as they look over the village. It's a silent yet powerful form of comfort.