Well, he could change a lot of things. Maybe he'd prevent some of the big battles or save some characters who died in the original timeline. For example, he might stop Frieza from destroying Planet Vegeta earlier. It would also be interesting to see how his Ultra Instinct powers interact with the past events and characters who haven't seen such power before.
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.
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.