1.) You cannot MAKE a Pokemon shiny. The only way to get a Pokemon that is shiny is to capture one in the wild, which is still a very slim chance of happening.
2.) Shiny Pokemon are no different than any other Pokemon regarding stats. The only way a Shiny Pokemon might be different is if it is an event Pokemon and even then, I'm not sure how they would be different.
3.) The Shiny Stone does not make a Pokemon Shiny, as Ultimate DarkraiFan stated, otherwise there would be n00bs everywhere imaginable saying "OMGZ, GIVES M3Z A SHNYZ STN!!!1!"
4.) Shiny Stones were not brought in until Diamond/Pearl/Platinum and are used to evolve certain Pokemon.
Yes, I know this question is several months old, but there was so much that needed to be answered here, it bugged me to no end.