No, they're completely different hacks.
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The Shiny Stone does not exist in Pokemon Gold, Silver and Crystal it was added when Diamond and Pearl came out and if you're referring to Pokemon HeartGold, the Shiny Stone can be found at the National Park and can be won if you come in 1st place in the Bug Catching Contest.
In the 2nd generation games (Gold/Silver/Crystal), the offspring will have a 1/64 chance of being shiny. In later generation games, the chance of getting a shiny offspring is the same as encountering a wild shiny Pokemon.
A golden Margikarp is a shiny margikarp, and as with other shiny Pokemon, there is only a 1/1892 chance of getting a Shiny(golden) magikarp. Breeding a Shiny Gyarados or a Shiny margikarp with another shiny Pokemon THAT CAN BREED WITH GYARADOS/MARGIKARP may have a higher chance of breeding a shiny magikarp. You can also trade the shiny gyarados from Pokemon Gold, Silver, and Crystal version.
If your legendary Pokemon run away in Shiny Gold, there is no way of retrieving them again.
If you can trade Pokemon from crystal version to gold version my guess is yes