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.
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.
A theme of acceptance is also prevalent. Loki is often seen as an outcast, and Odin's love can represent acceptance of Loki's true self, whether it's his magical abilities, his different nature compared to the other Asgardians, or his past mistakes. This acceptance can be a slow and arduous process in the fics, full of emotional ups and downs.
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.
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.
One great 'odin loves loki fanfic' is 'A Father's Unspoken Love' on FanFiction.net. It delves deep into Odin's complex feelings for Loki, exploring their relationship from a more emotional and psychological perspective.
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.