I wouldn't say it is useless, although it doesn't seem particularly useful. You may pay an action token now to receive possibly several action tokens in the future (by defeating several troublemakers at the problem and possibly again when you are in a problem faceoff at the problem). As a strategy, this is troublesome because of the opportunity costs of using the action token in the first place, the uncertainty of winning the final problem faceoff, and the fact that your opponent may not play multiple troublemakers at the problem to avoid giving you additional bonuses.
Here is the scenario where I would be inclined to play this card: It's the main phase and I now have what I consider to be an acceptable power at the troublemaker to win the faceoff next turn. I have a remaining action token after playing all of the other cards I wanted this turn. I can spend that action token now and I can expect to get it back during the troublemaker faceoff next turn. After that, I will have the opportunity to continue to collect additional action tokens for wins at the problem.
As for your second question, winning a faceoff with the card at a problem will earn you one action token plus the normal amount of bonus points.