One common theme is redemption. When Loki is hurt, it often serves as a catalyst for him to seek redemption. For example, in many fanfictions, his physical or emotional pain makes him re - evaluate his actions and strive to be a better person.
There's also 'When Loki is Hurt' which is quite popular. In this fanfic, Loki gets injured during a battle and it shows how his friends and foes react to his vulnerable state. It's an interesting exploration of his character in a difficult situation.
One common plotline is Loki getting hurt during a battle. Maybe he's outnumbered by enemies and sustains serious injuries while trying to protect Asgard or his loved ones. Another could be Loki getting hurt as a result of a betrayal, like someone he trusted stabbing him in the back, literally or figuratively. And sometimes it's self - sacrifice, where he endures harm to save others, which then leads to a journey of recovery and self - discovery.
In some fanfictions, Jane Foster could play a role. If she's around Asgard at the time, being a scientist, she might have some knowledge or technology that could be used to treat Loki's wounds. Also, Valkyrie could be a helper. She's a fierce warrior and has a sense of honor. She might see Loki's injury as a chance to prove her worth or as a debt she needs to repay if Loki had previously helped her in some way. And of course, Frigga, if she were still alive in the fanfiction, would be a great source of comfort and healing magic for Loki.
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.
He wasn't sure. The information I know about the source and background of the Ao Ao awaiting arrest comic is very limited. It could be adapted from a novel or an original. If you can provide more information about the manga, I will try my best to answer your questions.
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.
He could meet the Frost Giants. Since he has some connection to them already, they might welcome him or at least be intrigued by his presence. He could learn more about his heritage from them and maybe even form an alliance.