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.
There would be a lot of implications for Goku's character growth. In the original story, Goku's journey to achieving Ultra Instinct was a long and arduous one filled with many battles and self - discoveries. If he was born with it, he would lack that growth experience. However, he could still have other forms of growth, like learning to control his emotions better while using Ultra Instinct. His relationships with his family and friends might also be different. For instance, Chi - Chi might be more worried about his safety since he has such a powerful ability from birth, and Gohan might look up to him even more. It could also change how Goku views himself. Instead of seeing himself as a constantly evolving warrior, he might feel a greater sense of responsibility due to his inborn power.
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.