Friendship - turned - more - than - friends is also quite common. They start as colleagues or friends in the 'Jujutsu Kaisen' universe, and in fanfics, it often evolves into a deeper relationship, whether it's romantic or a very close platonic bond with strong feelings. Another theme could be their shared experiences in battles. How they rely on each other in dangerous situations and how that affects their relationship off the battlefield.
Sure. You can check out Archive of Our Own (AO3). There are a lot of great 'nanami x gojo' fanfics there. Just search for the 'nanami x gojo' tag, and you'll be presented with a wide variety of stories written by different authors, with different plotlines and writing styles.
Toge Inumaki is important too. His special cursed speech ability makes him stand out. Also, the principal of the school, Masamichi Yaga, is likely to be important as he is in a position of authority and has an influence on Gojo and the other students. There could be other characters like the members of different clans that also play roles in the complex web of the story.