Yes, any Pokemon can be shiny when it can be hatched from an Egg, including Geodude.
A gold geodude is just a shiny geodude you must keep finding geodude in granite cave until its shiny.
What you have encountered is a shiny Geodude, which, as you described, is gold and a normal Geodude is a light gray color. Think of shiny Geodude as a gold nugget and a normal Geodude has a regular rock.
You can't
You could just go to challenges and win to get a shiny geodude!
5234: Shiny Pidgey 5231: Shiny Geodude (once) 5231(space): Shiny geodude as many times as you want Shiny pikachu 0.05% chance of it appearing on veredant forest 1 or 2
If you mean a Shiny Geodude, they appear randomly and very rarely and there's no specific way to get it.
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5234- Shiny Pidgey 5231- Shiny Geodude 673034- Shiny Jigglypuff
Anywhere you can find geodudes, but they are extremily rare.
where ever you find geodudes one could be shiny i found a shiny before my first gym it was in Oreburgh Gate on Pearl
well there are no common shiny Pokemon in heart gold but i have seen a shiny garados's and a shiny medapod. so maybe garados.
okay i will trade you spinda