If you want to cast a card this way, you cast it as part of the resolution of Maelstrom Angel's triggered ability. Timing restrictions based on the card's type (such as creature or sorcery) are ignored. Other casting restrictions are not (such as "Cast [this card] only before attackers are declared").

If you cast a card this way, you're casting it as a spell. It can be countered.

If you cast a card with X in its cost this way, X must be 0.

If you cast a card "without paying its mana cost," you can't pay any alternative costs, such as evoke or the alternative cost provided by the morph ability. However, you can pay optional additional costs, such as conspire, and you must still pay mandatory additional costs, such as the one on Goldmeadow Stalwart.