Imminent Doom's triggered ability resolves before the spell that caused it to trigger. The ability will resolve even if that spell is countered.

If a spell has {X} in its mana cost, include the value chosen for that X when determining the mana value of that spell.

The amount of damage Imminent Doom's triggered ability deals is the number of counters it had on it as the ability triggered. For example, if you cast Shock and then respond to Imminent Doom's triggered ability with a second Shock, both abilities cause Imminent Doom to deal 1 damage and Imminent Doom will end up with three doom counters on it.