Sure, Megumi discovers the truth about Toji being his dad in the manga. It's a crucial plot point that brings about various changes in Megumi's storyline and his relationships with others.
Another theme is growth. Megumi's growth as a person and as a sorcerer is often tied to his relationship with Gojo. In these fanfics, Gojo's influence helps Megumi become stronger, not just in terms of his abilities but also in his emotional maturity. For instance, Gojo might teach Megumi how to handle difficult situations, which in turn helps Megumi grow. And of course, the theme of love is there. It might not be a romantic love, but the love between a father and son. Gojo's care for Megumi and Megumi's acceptance of Gojo as a father figure is a central part of these fanfics. It gives a warm and fuzzy feeling to the readers.
Sure does! Baki beats his dad in the manga. It's a climactic moment that showcases Baki's determination and the culmination of his hard work and development throughout the story.
I'm not sure about the name exactly, but there are some fanfics where Megumi calls Gojo dad in a more action - packed setting. For example, in some where they are fighting curses together. Megumi's respect for Gojo as a father - like figure is shown through their teamwork and how Gojo protects Megumi during battles.
Maybe his dad gives a small smile and a nod. He could be a bit reserved in his reactions but still show that he appreciates Adrien's attempt at humor. He might say something like 'That was quite clever, Adrien.'
He interacts with his family in various ways. He scolds his son Ralphie when he misbehaves but also shows love and support. He participates in family activities like Christmas dinner.