Thor's perception of Loki would change drastically. Instead of seeing him as his mischievous but ultimately Asgardian brother, he would start to view Loki as an outsider, an enemy perhaps. This change in their relationship would affect Thor's self - confidence. He might become more hesitant in his actions, constantly wondering if he could have done something different to keep Loki in Asgard. Also, he would have to face the political implications within Asgard, as some might see Loki's stay in Jotunheim as a threat and put pressure on Thor to take action.
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.
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.
His character could also develop in terms of his powers. Maybe the abandonment was related to his latent magical abilities. He could start exploring and mastering his powers more in the fanfic. Thor's presence could either be a hindrance or a help. If it's a help, Thor could encourage Loki to use his powers for good, which would be a big step in Loki's character development.
If Loki survived in Infinity War fanfiction, it could have led to a very different outcome. He might have used his trickery to deceive Thanos in some way. Maybe he could have pretended to be on Thanos' side while actually working against him. This would have added an extra layer of intrigue to the story as the other characters would have been unsure of his true motives.
Another way is that Thor teams up with other allies. Maybe he gets help from the Avengers or some other powerful beings from the Marvel universe. They could create a diversion while Thor sneaks in to save Loki. Thor could also use his battle experience and strategic thinking. He might figure out Thanos' weak points and use that knowledge to rescue Loki. For instance, if Thanos has a certain device that is powering his hold on Loki, Thor could destroy it.
Perhaps Loki is forced to stay in Jotunheim. There could be a powerful spell or curse that binds him to the realm. This could lead to an interesting plot where Thor has to find a way to break the spell and rescue Loki. It would also give Loki a chance to explore his identity while being stuck there.
One common theme could be redemption. After experiencing abuse, Loki might be on a journey to redeem himself or find a way to heal. Another theme could be power dynamics. The abuse might be related to power imbalances between Loki and Thor, which can be explored in different ways. And also, the theme of forgiveness could play a role, either Loki seeking forgiveness from Thor or vice versa.
Well, it can be a way to bring more diversity to the fanfic world. It allows fans to explore different aspects of Loki's character that might not be explored in the official Marvel stories.