No, the Dream World is not available for Pokémon Platinum, the Dream World is only available for Pokémon Black, Pokémon White, Pokémon Black 2 and Pokémon White 2.
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the dream world is where you can get pokemon from different generations.
in the distortion world i guess you can also get it underground
You will need to trade it from Pokemon White. Or you can get it at Spooky Manor in the Dream World (Over 10,000 dream points).
Lopunny cannot be found in Dream world, but Buneary can-In the pleasant Forest after earning at least 7500 dream points
The Distortion world is only available in Pokemon Platinum