If the spell requires any targets, those targets are chosen when the spell is finally cast, not when it’s exiled.

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 during the card’s owner’s next upkeep.

When the last time counter is removed, the second triggered ability of suspend will trigger. It doesn’t matter why the last time counter was removed or what effect removed it.

If the second triggered ability of suspend (the one that lets you cast the card) is countered, the card can’t be cast. It remains exiled with no time counters on it, and it’s no longer suspended.

As the second triggered ability resolves, you must cast the card if able. Timing restrictions based on the card’s type are ignored.

If you can’t cast the card, perhaps because there are no legal targets available, it remains exiled with no time counters on it, and it’s no longer suspended.

If the spell has any mandatory additional costs, you must pay those if able. However, if an additional cost includes a mana payment, you are forced to pay that cost only if there’s enough mana in your mana pool at the time you cast the spell. You aren’t forced to activate any mana abilities, although you may do so if you wish.

A creature cast using suspend will enter the battlefield with haste. It will have haste until another player gains control of it (or, in some rare cases, gains control of the creature spell itself).