Ore-Rich Stalactite // Cosmium Catalyst

You choose whether or not to cast the exiled card as Cosmium Catalyst's activated ability resolves. If you do, you do so as part of the resolution of that ability. You can't wait to cast it later in the turn. Timing restrictions based on the card's type are ignored.

If you cast a card "without paying its mana cost," you can't pay any alternative costs. You can, however, pay additional costs. If the card has any mandatory additional costs, those must be paid to cast the card.

If the materials required include multiple objects, you may exile some of them from among permanents you control and the rest from among cards in your graveyard. You don't have to choose all permanents or all cards from your graveyard.

If a card that isn't a transforming double-faced card becomes a copy of a card with craft, it'll stay in exile if you activate the craft ability. It won't return to the battlefield.