Maelstrom Archangel — ruling 1

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”).

Maelstrom Archangel — ruling 2

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

Maelstrom Archangel — ruling 3

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

Maelstrom Archangel — ruling 4

If you cast a card “without paying its mana cost,” you can't choose to cast it for 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.

Maelstrom Archangel : règles, fonctionnement et interactions (MTG)

Maelstrom Archangel is one of those cards players keep asking about. Here is, in plain words, what its official text says, the rulings published by Wizards of the Coast, and the combos players actually run.

Official card text

Flying Whenever this creature deals combat damage to a player, you may cast a spell from your hand without paying its mana cost.

How it works : Maelstrom Archangel

Original English text — Wizards of the Coast / Scryfall

#1February 1, 2009· Wizards of the Coast
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”).
No other card is named in this ruling.
#2February 1, 2009· Wizards of the Coast
If you cast a card this way, you're casting it as a spell. It can be countered.
No other card is named in this ruling.
#3February 1, 2009· Wizards of the Coast
If you cast a card with X in its cost this way, X must be 0.
No other card is named in this ruling.
#4February 1, 2009· Wizards of the Coast
If you cast a card “without paying its mana cost,” you can't choose to cast it for 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.
No other card is named in this ruling.