One idea could be to focus on Bardock's perspective before his fateful battle. Maybe explore his thoughts about his son Goku being sent to Earth and his own impending doom. He could have some premonitions about Goku's future role in saving the universe.
It could be Vegeta. Maybe Vegeta does something really underhanded like stealing Goku's senzu beans or trying to take all the credit for a victory that Goku also contributed to. Goku, being a fair - minded person, would get angry at such behavior.
Definitely include Bardock's last stand. His heroic yet doomed battle is a crucial part of the Saiyan lore. It could be written in great detail, with Bardock using his full power against Frieza's forces.
Well, perhaps in the fanfiction, Goku gets mad when he discovers that someone has been using his name for evil deeds. This would go against his values of justice and protecting the innocent. He might get really angry and go on a search to clear his name and stop the impostor. Or it could be that a new, extremely powerful villain emerges and starts to destroy planets without any remorse. Goku, being the defender of the universe, would be enraged by such senseless destruction and would confront the villain with all his might.
One reason could be ChiChi's overbearing nature. She is often very strict about Goku's training and how he spends his time. In fanfiction, this could be exaggerated to the point where Goku finally gets fed up. For example, if she constantly nags him about not doing enough chores around the house instead of training, it might push Goku to his limit.
One common scenario is when his friends are in danger. Goku is extremely protective of his friends, and if he sees them being seriously threatened or hurt, he'll get mad. Another is when an enemy disrespects his family or the Saiyan race. Goku has a strong sense of pride in his heritage, and any slights against it can enrage him.
I haven't actually read this specific 'piccolo and gohan lemon fanfiction', but generally, in fanfictions involving these two characters, it might explore their relationship in unique ways. It could be about their friendship evolving, or perhaps their teamwork in new and unimagined scenarios within the Dragon Ball universe.
A major theme is identity. Since she is a female version of Piccolo, she has to come to terms with who she is compared to the original Piccolo. Family also plays a role. In some fanfictions, she might be searching for her family or creating a new family of her own. Additionally, the theme of good vs. evil is common, as she battles against various villains.
I'm not that familiar with the specific 'Brian Piccolo Thanksgiving Day story'. Maybe it could be about how he spent the Thanksgiving Day with his family, sharing a big meal and giving thanks. It might also involve some special traditions he had on that day.