In such fanfictions, Goku might develop by becoming more of a mentor to Gohan. He could teach Gohan new fighting moves and also how to control his emotions better during battles.
In a Gohan x Goku fanfic, their relationship can be delved into by creating scenarios where they have to rely on each other completely. For example, if they are in a situation where Goku's strength and Gohan's intelligence are both required to escape. Their different personalities can also be highlighted. Goku's carefree nature contrasted with Gohan's more studious and responsible side. And of course, flashbacks to Gohan's childhood and how Goku's presence or absence affected him can add depth to their relationship.
Yes, there are quite a few out there. You can start by looking on fanfic websites like FanFiction.net or Archive of Our Own. Just search for 'DBS Goku x Bulma' and you'll likely find some interesting reads.
One possible interaction is that Bardock could spar with Goku and Gohan. He'd test their limits and see how much they've learned about fighting. Another could be Bardock sharing stories of Planet Vegeta with them, which would be really interesting for Goku and Gohan to hear.
In the manga, Gohan never managed to defeat Goku. Their battles often ended with Goku coming out on top or the fight being interrupted for some reason.
One factor is the exploration of their relationship in different scenarios. In the canon, they have a long - standing friendship. Fanfics can take this and expand it, like what if Goku developed romantic feelings for Bulma? Or how would they handle a crisis together in a more intimate way than in the show? Also, seeing how the authors incorporate the Dragon Ball Super elements like the new forms and powers into the story of their relationship adds depth and interest.
A possible plot could involve Goku and Gine meeting in a parallel universe where the normal rules don't quite apply. They start off as strangers but quickly realize they have a lot in common. Their relationship could develop as they train together, learning from each other's fighting styles. Gine might introduce Goku to some unique Saiyan traditions that have been long forgotten, and together they become a powerful duo in this new universe.
Well, some fanfictions focus on Gohan and Goku's time - traveling adventures. They might go back in time to change certain events in the Dragon Ball universe. Also, there are fanfictions where they team up with other characters in unexpected ways. For example, they could form a team with villains who have a change of heart. These fanfictions often show how Gohan and Goku's different personalities interact in various situations.
In a fanfiction where Future Gohan meets Goku, it could be an emotional reunion. Gohan might be filled with a sense of relief and joy, seeing his father again. He could show Goku all the things he's been through in the future, and Goku would be both proud and sad about what his son has endured.
You can focus on their emotional bond. For example, show how Goku's pride in Gohan's growth and achievements affects their relationship. It could be about Gohan seeking Goku's approval and Goku being there to give it wholeheartedly.