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.
Well, it depends on the author's imagination. Some fanfics might show ultra instinct as an overwhelming power, while others might have a more nuanced take.
There are indeed Naruto fanfictions where he has Ultra Instinct. Fanfiction writers like to experiment with different power combinations. By giving Naruto Ultra Instinct, they can create really exciting battle scenes. For example, Naruto could use Ultra Instinct to dodge attacks more effectively during a fight with a powerful enemy like Madara, adding a whole new dimension to the story.
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.