A good one often has a clear goal for the main characters. For example, in 'Naruto', Naruto's goal to become Hokage drives the story. This gives a clear direction and makes the story thrust forward as he faces obstacles on his way.
I'm not aware of any specific 'anime thrusting fanfic' that I can recommend. Such content might not be in line with the general values of the anime community. Instead, you could look for fanfics that center around the relationships between characters in a more positive and healthy way. For instance, fanfics about friendship growth or how characters form alliances to face common enemies.
No. The anime community generally values positive, creative, and family - friendly content. Fanfics that involve 'thrusting' are likely to be considered inappropriate and not in line with the community's standards. Most anime enthusiasts prefer fanfics that enhance the original story, develop characters further, or explore interesting concepts within the anime's world.
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.