Yes, any card that evolves automatically (Rare Candy), breaks the rules of normal evolution, such as evolving after the pokemon has been in play for a turn and no evolving on the first turn.
Yes, you must put at least one card from your hand to the bottom for your deck to activate Cosmic Power. In this game, "up to" usually means "up to, but at least one". It's weird, but that's how it works.