Alolan Geodude, the rock Pokémon from Alola, can be found in the wild in Pokémon Go. Yes, Geodude can be shiny in Pokémon Go!
Alolan Geodude actually had its own Community Day in May 2022, so many Pokémon Go collectors probably have a shiny or two from that event. Alolan Graveler is a fine rock-type attacker when it comes to gyms and raids, though it's outclassed by many other rock-type Pokémon, like Tyranitar and Rhyperior.
As per The Silph Road, the shiny rate for Pokémon on a regular day is approximately one in 500. As of writing this, the jury is out on Alolan Geodude's shiny rate. While other Alolan Pokémon have a boosted (1 in 64) shiny rate, there's not enough data on Alolan Geodude to confirm this or not.
Not much, unfortunately. It appears to be random chance. Shiny Pokémon catch rates are set by developer Niantic, and they are typically only boosted during special events like Community Days or Safari Zones, or in Legendary Raids. There are no consumable items that boost shiny Pokémon rates.
LeekDuck keeps a list of currently available shiny Pokémon. It's a helpful visual guide that illustrates what all of the existing shiny Pokémon look like.
For more tips, check out Polygon's Pokémon Go guides.