One factor that makes a Kakashi fanfic cute is when it focuses on his relationships. For example, if it shows his interactions with his students like Naruto, Sasuke, and Sakura in a more light - hearted and affectionate way. Maybe Kakashi giving them small gifts or just being there for them during a difficult time in a really sweet manner.
The plot could be that Naruto gets a special mission to protect Kakashi's face from a group of rogue ninjas who want to steal Kakashi's identity. Naruto has to use his unique skills to fend off the attackers and keep Kakashi's face safe.
A possible plotline could be that a new enemy targets Kakashi because of his distinct face features, believing there is some hidden power in his appearance. Naruto then has to protect Kakashi. Another plotline could be a magical spell that gets cast on Kakashi's face, changing his expressions uncontrollably, and Naruto tries to find a way to break the spell.
There is a fanfic titled 'Kakashi and the Kitten'. In this, Kakashi finds an abandoned kitten and decides to take care of it. It shows his softer side as he tries to figure out how to take care of the little furry friend. The way he interacts with the kitten is just so cute. Also, 'Cute Encounters with Kakashi' might be a great one. It could be about different people in the village having unexpected and cute encounters with Kakashi, like a child asking him for help with a small task and Kakashi being really patient and kind.
Some fanfictions might introduce new, original villains. For example, a dark sorcerer - type character who wants to use Naruto's unique chakra for his own evil purposes. Kakashi has to face this sorcerer and his minions to keep Naruto out of harm's way.
Well, for starters, Kakashi has to deal with Naruto's hyperactive and sometimes reckless behavior. Naruto often acts without thinking, which could put him in danger. Sasuke, with his complex emotions and the burden of his clan's massacre, is also a handful. Kakashi needs to make Sasuke understand that revenge is not the only way forward. Additionally, Kakashi has to ensure that both Naruto and Sasuke get along well with each other. There could be rivalry between them, and Kakashi has to manage that in a way that doesn't harm their relationship or their growth as ninjas.
The relationship could be developed through a shared love of food. Maybe the genin are all food enthusiasts and Kakashi, who usually doesn't show much interest in food, starts to enjoy cooking with them. They bond over trying new recipes and sharing meals, which in turn makes their ninja training sessions more enjoyable and productive.
One great fanfic could be one that focuses on Kakashi's face and how Naruto is inspired by his calm and confident expressions. Maybe it shows Naruto trying to imitate Kakashi's facial expressions during a tough battle to boost his own morale.
In the fanfiction, Kakashi might face the challenge of Naruto's insecurities. Naruto has always had a complex about being alone and not having a family. Kakashi would have to find ways to make Naruto feel secure and loved. Also, dealing with Naruto's powerful and sometimes uncontrollable chakra could be a problem. Kakashi would need to train Naruto to master his chakra properly without it overwhelming him.