Animar's triggered ability resolves before the creature spell that causes it to trigger. The ability will resolve even if that spell is countered.

To determine the total cost of a creature spell, start with the mana cost or alternative cost you're paying, add any cost increases, then apply any cost reductions. The mana value of the creature remains unchanged, no matter what the total cost to cast it was.

Animar's triggered ability triggers only when a creature spell is cast, after costs are paid. The counter put on Animar for a creature spell won't affect the cost of that creature spell, only future ones.