Similar to wild Reshiram, Zekrom and Victini in Pokémon Black and White, all Pokémon found in the Dream World cannot be Shiny. A Pokémon found in the Dream World will always have its Hidden Ability, if it has one. Pokémon found in the Dream World have about a 25% chance of being female regardless of gender distribution, unless the Pokémon can be of only one gender. All Pokémon obtained in the Dream World will be at level 10, unless they evolve at a level above 10, in which case they will be at that level; certain legendary Pokémon will also be at levels above 10.
Yes you can with events, they are releaseing every legendary dream world Pokemon event sometime in may through to december as well as the other events like gensect etc.
Hope I helped