I think I understand how this card works, but I want to check my interpretation.

Each time the attached character gets a focus token placed on it, it receives a damage, right? That seems really powerful for an enhancement that costs 0.

I originally thought the character received a damage only the first time it got focus tokens placed on it, but since the reaction can happen multiple times that should mean that any time focus tokens are placed on the character it receives damage, right?

Looks like you have it right. Note that if multiple focus tokens are placed simultaneously (commited to the force or a unit with multiple tactics striking) then it's still only 1 damage.

The victim takes damage whenever they take focus for ANY reason, yes? Focusing to strike, tactics, generating resources, focused by a card effect, focusing to pay the cost of some effect, ANYTHING?

Yep.