The Wolves are tapped as part of the activated ability’s effect, not as a cost.

If the targeted creature is an illegal target by the time the activated ability would resolve, the entire ability is countered. Nothing else happens. (For example, the Wolves aren’t tapped.)

The Wolves deal their damage first. This may be important if the damage causes the targeted creature’s power to be reduced (if it’s Protean Hydra, for example). However, creatures aren’t destroyed for having been dealt lethal damage until a spell or ability has finished resolving. If the targeted creature is dealt lethal damage by the tapped Wolves, it will still get to deal damage to those Wolves before being destroyed.

Only a Wolf creature tapped as part of the ability’s effect can be dealt damage by the targeted creature.

The targeted creature’s controller doesn’t divide that creature’s damage as the ability is activated (since the Wolves that will receive that damage aren’t targeted), so that player does so as the ability resolves. Each Wolf chosen by that player must be dealt at least 1 damage. There is no time to react between the time a Wolf is chosen, the time damage is dealt to it, and the time it’s destroyed for having been dealt lethal damage. If you want to put a regeneration shield on one of those Wolves, or target it with a damage-prevention spell, or anything else, you must do so before the ability resolves (and before you know which Wolves will be chosen and how much damage will be dealt to them).