One common theme is redemption. Loki often tries to redeem himself in Odin's eyes. Another theme is family. Their relationship as father - son is explored, whether it's a strained one or a reconciled one. And power is also a theme. Loki's desire for power and how Odin's power affects their relationship.
Loki might react with anger. He could seek revenge against Odin, plotting ways to undermine his power or expose his wrongdoings. This reaction is common as it shows Loki's pride and his unwillingness to be a victim.
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.
When Thor is mean to Loki in fanfiction, it can lead to a downward spiral in their relationship. Loki, feeling constantly attacked, may lash out in more extreme ways. Thor, on the other hand, may double down on his meanness, believing it's the only way to deal with Loki. This can create a cycle of animosity where any love or brotherly bond they had is overshadowed by anger and distrust. For example, Loki could start to form alliances with Thor's enemies out of spite, and Thor would see this as confirmation of Loki's untrustworthiness, making the relationship even worse.
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.
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.
One common theme is redemption. Maybe Odin is trying to make up for past wrongs towards Loki. Another is family drama, as their relationship is complex in the original mythology.
Yes, there are quite a few. You can start by looking on popular fanfiction websites like Archive of Our Own. There, you'll find various takes on the 'odin loves loki' concept. Some might explore it in a more platonic way, while others could be more on the romantic side.