Well, characters who had a rough start in the village due to Sandaime's decisions might be likely to support the bashing. For example, Naruto himself could be one. Given his difficult childhood with little support from the village at first, which some might blame on Sandaime, he could be portrayed as having negative feelings towards him in these fanfictions.
In a 'Naruto kills the Sandaime' fanfic, it would be a very dark and alternate take on the Naruto universe. This goes against the traditional bond and respect Naruto has for his village elders. It could be a result of some extreme corruption within the village that Naruto discovers, leading him to take such a drastic step. However, this is a huge deviation from the original storyline.
One possible fanfiction could be about the Fifth Kazekage's adventures in the Hidden Leaf Village after forming an alliance with Naruto. They might team up to face a new threat that neither of their villages could handle alone.
Obviously, Naruto and the Kazekage are the main characters. Naruto, with his determination and powerful jutsus, and the Kazekage, who represents the power and mystery of the Sand Village.
One possible story could be that Sakura goes to the Sand Village for a medical mission while Gaara is Kazekage. They start to interact more, and Gaara is impressed by Sakura's strength and kindness. Eventually, they form a strong friendship that helps in strengthening the bond between the Leaf and Sand villages.
One possible storyline could be that Naruto is chosen as a temporary Kazekage due to a threat that requires his unique skills. He then has to deal with internal conflicts within the Sand village while also facing external enemies. Another could be that there is some kind of prophecy that only Naruto can fulfill as Kazekage to save both Konoha and Suna.
Yes, there could be such a fanfiction. It might be about Naruto taking on the role of the Kazekage for some reason. Maybe there's a plot where Konoha and Suna form an even closer alliance and Naruto is sent to Suna to lead as Kazekage for a time. This could lead to all sorts of interesting scenarios, like Naruto having to deal with the different political and cultural aspects of Suna compared to Konoha.
Another theme is redemption. Since some Kazekage characters may have made mistakes in the past, fanfictions might show them trying to make up for it and regain the trust of their people. It can be a very emotional and character - building journey.
Character interaction. Sakura and the Kazekage usually have very distinct personalities, so seeing how they interact, whether it's in friendship or something more, is a key element.
In a fanfiction where the Sandaime survives the Chunin Exams, Konoha would be a very different place. His wisdom and experience are invaluable. He might be able to prevent some of the internal strife that occurred after his death. Naruto would probably grow even faster under his continued guidance. And the relationship between the different ninja clans might be more stable with his leadership still in place.