In some comic storylines, Loki does have a girlfriend. But it depends on the specific comic run and version of the character. Sometimes these relationships are short-lived or complex.
Loki might become more empathetic. Usually seen as a bit of a trickster, having a girlfriend could make him understand others' feelings better. For example, he'd have to consider her emotions when planning his schemes. He could also become more protective, using his powers not just for his own gain but to keep her safe.
One possible plotline could be that Loki meets a girl in a different realm. Maybe she's a powerful sorceress who initially challenges him. As they cross paths more often, they start to see each other's true selves. Loki, who is used to being alone and distrusted, slowly opens up to her. Their relationship could be filled with banter and magical adventures as they face threats to their realms together.
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.
Writers can also depict Loki as a character who is on a journey of self - discovery. His intersex nature is just one part of who he is, but it has a significant impact on how he views himself and his place in the world. He could start off as a more withdrawn character, but as the fanfiction progresses, he becomes more open and confident, especially with Thor by his side. The fanfic could explore how Loki's intersex identity shapes his relationships not only with Thor but also with other Asgardians.
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.
Loki could also show signs of fear, though he would try to hide it. Inside, he knows the power that Thanos wields. But on the outside, he would maintain a facade of bravado. His reactions would be a mix of his natural cunning and the instinct to survive in a very dangerous situation.
He might ally with Arya Stark. Loki would see her determination and skill, and they could form an unlikely partnership. Arya could learn some new tricks from Loki's magic, and Loki could use Arya's knowledge of Westeros to his advantage.