Takashi Komuro is a very popular character to focus on. He's the main protagonist in the original and has a lot of leadership qualities. His relationship with Rei Miyamoto also provides a lot of room for character development in fanfiction. Another popular character is Saeko Busujima. Her combat skills and her complex personality make her an interesting character to explore further.
One idea could be to explore the backstories of the minor characters in more depth. For example, the story could focus on a side character's journey before the zombie apocalypse and how they've changed since then. Another plot could be a survival story that takes place in a different location than the original, like an isolated island where they have to deal with not only zombies but also limited resources.
Naruto's experience in dealing with tough opponents in his own world would help him in the zombie - filled Highschool of the Dead. He would be able to quickly analyze the situation, figure out the weaknesses of the zombies, and come up with effective plans. His friendship - first approach might also lead to some interesting relationships with the other characters in this new and dangerous world.
The status of the Highschool of the Dead manga is rather unclear. There were some issues related to the author or publisher, and it just stopped without a definite conclusion.
Well, first of all, the writers often take the unique elements from each universe. From Naruto, it's the ninjutsu, kekkei genkai, and the concept of the ninja villages. From Highschool of the Dead, it's the zombie apocalypse and the school environment. They then find ways to make these elements work together. Maybe a character with a Sharingan from Naruto can use its powers to detect zombies from afar. Also, they might use the character relationships. A Naruto character could form a team with some Highschool of the Dead survivors to face the challenges together. And they might also play with the different values of the two universes. For example, the loyalty in Naruto and the survival instinct in Highschool of the Dead.
One possible aspect of such a fanfiction could be the combination of Naruto's ninja skills in the zombie - infested world of Highschool of the Dead. For example, Naruto's shadow clone jutsu could be used to distract the zombies while the characters from Highschool of the Dead search for supplies or a safe place. His ability to move quickly and stealthily like a ninja would also be a great advantage in that dangerous setting.