I was wondering if there’s a way to check what qualities a character with a known name has, or to "poll" a quality and see who has it.
You can’t do the former at all, to the best of my knowledge. For the latter, you can use “Broadcast living stories” to see how many people have a quality at a certain level, and if you actually broadcast something to them it’ll tell you how they are - but obviously you don’t want to send them stuff unless you actually want to send them stuff!