One plot idea could be Yami going on a solo mission to a mysterious and dangerous land. He has to face powerful new enemies and discover secrets about his own past. Another could be Yami training a young and inexperienced magic knight, sharing his unique combat and magic knowledge.
Yami remains alive in the manga. The author chose to keep Yami as an ongoing character to drive the story forward and interact with other characters in various scenarios.
As far as I know, Yami doesn't die in the manga. The story might have twists and turns, but that particular event hasn't happened yet. Maybe there are rumors or speculations, but based on the official storyline, no.
To write a believable characterisation of Yami, focus on his rough exterior but also his loyalty to his squad. Show his love for food, especially Japanese food. Also, don't forget his unique magic style and how he uses it in combat.
One common theme is adventure. Given their abilities and the worlds they come from, many fanfictions send them on exciting quests. For example, they might be on a journey to find a lost magical artifact.
Well, if Yami is abusing Yugi in fanfiction, it could be a sign of a darker or more complex take on their relationship. It might be exploring themes like power imbalance or psychological abuse. However, it could also be a misinterpretation or a way for the author to create drama.