I know for sure you can play Broken Time-Space on your first turn, I'll come back with the ruling on Rare Candy in just a second.
EDIT: OK, so the answer on Rare Candy is that even with Broken Time-Space in play, you may not play Rare Candy on your first turn or on a pokemon you just put into play. Even though Broken Time-Space gets around the normal evolution mechanic, Rare Candy specifically says that you "can't play this card on your first turn or on a Basic Pokemon that was just put into play this turn."