Collector's Cage

If you cast a spell "without paying its mana cost," you can't choose to cast it for any alternative costs. You can, however, pay additional costs, such as kicker costs. If the spell has any mandatory additional costs, those must be paid to cast the spell.

Any player who has controlled a permanent with a hideaway ability since a card was exiled with it may look at that card.

You choose whether to play the exiled card as Collector's Cage's last ability resolves. If you do, you do so as part of the resolution of that ability. You can't wait to play it later in the turn. Timing restrictions based on the card's types are ignored. However, you can never play lands on other players' turns.