The chance of a Pokemon received from an in-game trade being shiny is the same as the chance of capturing a shiny Pokemon in the wild.
You either find them randomly, or you use a chain with the pokeradar :)
Sadly it doesn't work that way with Shinys. Your chances of getting a shiny are 1/8192. This applys to wild encounters and breeding, even if the parents are both shiny.
no unless you use a cheat but they are very hard to find
yes they do