What happens when, and can I return face-down non-creature cards to my hand?
Yes, you can return the face-down card to your hand, and yes, you do have to reveal it.

The first rule about Manifest, 701.31a says


  "Manifest [a card]" means "Put [that card] onto the battlefield face down." That permanent is a 2/2 creature with no text, no name, no subtypes, and no mana cost. That permanent is a manifested permanent as long as it's face down. The effect defining its characteristics works any time the card is face down and ends when it's turned face up.


In addition, rule 707.9 says


  If a face-down permanent moves from the battlefield to any other zone, its owner must reveal it to all players as he or she moves it. If a face-down spell moves from the stack to any zone other than the battlefield, its owner must reveal it to all players as he or she moves it. At the end of each game, all face-down permanents and spells must be revealed to all players.