Uniquely identify means you can identify the specific person or thing — not just a category. Just knowing someone is an “actor” isn't enough, because there are lots of actors. But if you can name their role in a specific movie or recognize them by sight, that’s uniquely identifying — so check the box!
Already knew existed means you knew the person or thing existed before you started the quiz. If you see the soundtrack to a movie you know, and could have guessed that the soundtrack existed but had never known it, do not check the box.