>Does Steven really give you a villa in platinum?
Why did I say technically? Steven does not directly give it to you, rather a random trainer does. However it is hinted that Steven was the one who gave it to the trainer, who then gave it to you. I got one myself and wasted money on it.
>When the player arrives in the Resort Area, the villa is given to the player by its previous owner. The player can then purchase items from a catalog on the table.
>And do you actually get to meet caitlyn in platinum, a game that was made before unova existed?
In the Platinum/SoulSilver/Heartgold games Caitlin is in fact a member of the Battle Frontier (Caitlin is the correct spelling). She is the head of the Battle Castle.
>She is also the head of the Battle Castle in the Battle Frontier that appeared in Pokémon Platinum, HeartGold and SoulSilver.