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.
That really depends on personal preference. However, some popular ones often have a great balance between action and character development. For example, stories that explore how Goku's relationships change after getting Ultra Instinct can be really engaging.
A fanfiction could focus on Goku's relationships while in Ultra Instinct. For example, how does he interact with his friends and family? Does Vegeta view him differently? In this story, Goku might struggle to control the Ultra Instinct around his loved ones because it makes him seem so detached. This could lead to some interesting emotional moments between the characters.