In fanfiction, her character is distinct from Thor and Loki. Thor is associated with honor and strength in combat, Loki with his slyness and intelligence in manipulation. Their sister can be seen as a bridge between their two extremes. She may not be as physically strong as Thor but has her own form of power, perhaps in the realm of diplomacy or magic that is different from Loki's. For example, she could use her magic to create harmony rather than chaos like Loki. Also, her motivation might be different. Instead of Thor's quest for glory or Loki's desire for power, she could be driven by a need to protect her family and the realms in a more holistic way.
Well, one possible plot could be that Thor and Loki's little sister has some special powers that are a mix of their own. She might be caught in the middle of their feuds, trying to bring peace between them. For example, she could use her powers to stop Loki from his mischievous plans that would anger Thor, while also making Thor understand Loki's motives better.
It could be Malekith. He might see the sister as a way to get to Thor and Loki and gain power over Asgard. Since she's a new and potentially vulnerable target, he could try to use her in his dark schemes.
There are quite a few fanfictions out there. In some, she is a powerful sorceress like Loki. For example, in 'Sorceress Sister', she uses her magic to help Thor in battles against dark forces. Some fanfictions also explore her relationship with the other Asgardians. In 'Asgardian Bonds', she forms new alliances and friendships within the realm while also reconnecting with her brothers.
Thor might initially go into denial. He can't believe that Loki is truly gone. He may hold Loki's body for a long time, as if waiting for him to come back to life. Then, he could become angry. Angry at the situation, at whoever or whatever caused Loki's death. Eventually, he may find solace in the memories of Loki. Remembering the good times they had together and using those memories to move forward.
Y/N should have their own goals and dreams. If they're interested in becoming an Auror, that can shape their actions and decisions. Their reactions to Draco should be based on their personality. If they're a shy person, they might be more hesitant around him. And make sure their dialogue is natural. Don't make them say things that are out of character just to move the plot along. For instance, if Y/N is a studious type, they're more likely to talk about books or spells when interacting with Draco.
Thor could also become very angry. Not at Loki, but at whatever or whoever caused those scars. He might vow to avenge Loki and seek out those responsible. For example, if the scars were from a battle with a particular enemy, Thor would be determined to confront that foe.
I'm not very familiar with this specific fanfic. However, generally, a fanfic about Loki and Thor might explore their complex relationship in the context of the Marvel universe. If Loki is intersex in this fanfic, it could add an interesting layer to the character's identity and how they interact with Thor.
In many Thor Loki Avengers fanfictions, Loki's character development often starts from a place of being the villain. He then gradually realizes the value of his relationships, especially with Thor. For example, in some stories, after seeing the loyalty of the Avengers to each other, he begins to question his own actions. He might start to show remorse for his past deeds like the attack on New York.