One idea could be exploring how Goku's Dark Instincts affect his relationships with his friends and family. Maybe they're initially scared or distrustful. Another is a battle scenario where Goku with Dark Instincts faces a powerful new enemy that only this darker side of him can defeat. And a third could be delving into the origin of these Dark Instincts, like if they were always there but dormant.
First, you should research about Goku's character and his existing powers and personality traits. Then, think about what the Dark Instincts would add or change. You could start with a simple scenario like Goku feeling a strange new power within him during a training session. Another way is to begin with a dream sequence where Goku is consumed by his Dark Instincts.
Yes, it is possible. In fanfiction, writers have the creative freedom to reimagine the origin of characters. Goku being born with Ultra Instinct can add a whole new layer to his character development. It could mean that his power growth would be different from the original story, perhaps faster or with different challenges along the way.
You could write a fanfiction where Goku teaches others about Ultra Instinct. Maybe he tries to pass on this power to Gohan or Trunks. This would involve Goku having to understand the power more deeply himself in order to teach it, and it would also be a great way to develop the other characters.
Goku definitely masters Ultra Instinct in the manga. This transformation gives him a huge boost in power and allows him to take on even stronger opponents.