Often, in 'Goku Harem Fanfic', Goku becomes more aware of his romantic side. He might be a bit more in tune with the emotions of the female characters around him compared to his original portrayal in the Dragon Ball series, where he was mostly focused on fighting and training.
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 other fanfictions, they could be rivals. Goku is always looking for a strong opponent, and Sailor Moon's unique powers could make her an interesting rival. They might have battles where they test each other's limits, but also learn to respect each other in the process. They both have strong beliefs in protecting their worlds and those they love, so even as rivals, they could end up on the same side when a greater threat emerges.
In some lemon fanfiction, their interaction can be filled with tension. Goku, being the good - natured Saiyan, may be initially wary of Frieza. But as the story progresses, they might find common ground. For example, they could start to respect each other's power.
Well, Vegeta would be a likely character. He might be initially suspicious of the female Goku. Maybe he thinks she's a threat or just can't believe there's another Goku - like being. He could be there to add some comical moments as he tries to understand the situation.
They likely have a loving relationship. As Saiyans, they would have a bond based on their race and their shared goals, perhaps related to the Saiyan pride and survival.
Writers often start by changing Goku's personality traits. Instead of his usual kind - hearted and naive self, they make him more cunning and self - centered. For example, they might have him using his powers for personal gain rather than to protect others.