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.
These fanfictions typically show their relationship as something that has to be hidden from the rest of Asgard. It adds an element of secrecy and danger. The relationship is also often portrayed as a way for both characters to find solace in a world that doesn't always understand them. Loki's cunning and Thor's power are intertwined in a way that makes their connection unique and captivating.
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.
There's 'Thor's Redemption in Loki's Arms'. In this story, Thor realizes his true feelings for Loki after a series of events that nearly tear Asgard apart. It's a tale full of emotion and character development.
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.
I really like 'A Different Path for Loki'. In this fanfiction, Loki is given a chance to redeem himself in a unique way. It's full of interesting plot twists and great dialogue between Thor and Loki. The author does a wonderful job of exploring Loki's psyche and his relationship with Thor against the backdrop of the Asgardian world.