You put one of your pokemon to sleep by Game Sync which can be found in your
C-gear, Then go to the Island Of Dreams (The Rainbow), Once you enter you will be in a place were you can take only 10 Steps to gather as many Items/Berries/Pokemon as you can, but to recieve the Pokemon, you will have to befriend them by playing and winning a game with them successfully, to befriend them. Then when your 10 steps has been used, you will End up at the Tree of Dreams where you can ''Buy'' as may Pokemon as you befriended with Berries. Once your finished, the Pokemon you Bought will be on the Friend board, And now you can wake up your pokemon with the ''Off'' sign on the Top-Right, And obtain your pokemon at the Entree Forest in Entralink.
No, they are not programmed to be Shiny, Unless you hack.
No, you will only obtain the Pokemon with 1 Ability which is the Hidden Ability.
4.Yes, the Hidden Ability will Replace the Normal Ability.
5.No, your Pokemon will wake up in it's Original Ability.
6.No you can only have 1 Ability, not all Three.
Hope this helps! XD