If you cast a card "without paying its mana cost," such as with suspend, you can't choose to cast it for any alternative costs. You can, however, pay additional costs. If the card has any mandatory additional costs, you must pay those if you want to cast the card.
You can exile a card in your hand using suspend any time you could cast that card. Consider its card type, any effects that modify when you could cast it (such as flash) and any other effects that stop you from casting it (such as from Meddling Mage's ability) to determine if and when you can do this. Whether you could actually complete all steps in casting the card is irrelevant. For example, you can exile a card with suspend that has no mana cost or that requires a target even if no legal targets are available at that time.
Suspend is a keyword that represents three abilities. The first is a static ability that allows you to exile the card from your hand with the specified number of time counters (the number before the dash) on it by paying its suspend cost (listed after the dash). The second is a triggered ability that removes a time counter from the suspended card at the beginning of each of your upkeeps. The third is a triggered ability that gives you the option to cast the card when the last time counter is removed.
Magic: The Gathering · ™ & © Wizards of the Coast · Illus. Cliff Childs
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The mana value of a spell cast without paying its mana cost is determined by its mana cost, even though that cost wasn't paid.
When the last time counter is removed, the second triggered ability of suspend (the one that lets you cast the card) triggers. It doesn't matter why the last time counter was removed or what effect removed it.
If the card has {X} in its mana cost, you must choose 0 as the value of X when casting it without paying its mana cost.
Cards exiled with suspend are exiled face up.
If the second triggered ability is countered, the card can't be cast. It remains exiled with no time counters on it, and it's no longer suspended.
Exiling a card with suspend isn't casting that card. This action doesn't use the stack and can't be responded to.
If the spell requires any targets, those targets are chosen when the spell is finally cast, not when it's exiled.
If an effect refers to a "suspended card," that means a card that (1) has suspend, (2) is in exile, and (3) has one or more time counters on it.
If the first triggered ability of suspend (the one that removes time counters) is countered, no time counter is removed. The ability will trigger again at the beginning of the card's owner's next upkeep.
If a card with no mana cost is given an alternative cost equal to its mana cost (by Snapcaster Mage, for example), that cost cannot be paid and the card cannot be cast this way.
A card with no mana cost can't be cast normally; you'll need a way to cast it for an alternative cost or without paying its mana cost, such as by suspending it.
Due to a recent rules change to suspend, you are no longer required to cast the suspended card as the second triggered ability of suspend resolves. Instead, as the second triggered ability resolves, you may cast the card. Timing permissions based on the card's type are ignored. If you don't cast the card, it remains exiled with no time counters on it, and it's no longer suspended.
If an effect puts an Aura onto the battlefield under your control, you choose what it enters attached to. It must be something that it could legally enchant, but not necessarily something it could target if it were on the stack. For example, you could attach an Aura with enchant creature to an opponent's creature with hexproof, but not to a creature with protection from enchantments.
All of the enchantment cards in your graveyard that can return to the battlefield will. You can't choose to leave some in the graveyard. If you're returning an Aura that can only be attached to a creature, but your opponent is the only player who controls a creature, you must choose to attach it to that creature.