Except in the exercise where you're transcribing from the Greek audio, because the speaker definitely says αυτή not αυτήν.
How is the singular "πληροφορία" used in Greek compared to its plural? Does it refer to a single fact or idea?
Yes. Πληροφορία usually refers to a single fact, whereas πληροφορίες refers to multiple ones, or information in general. ^.^
Surely: Εγώ δεν ήξερα αυτή την πληροφορία. = "I didn't know this information" would make more sense, since the information must now be known to the speaker?
Or maybe the first speaker just asked the second one if he knows something about a certain topic, and he replies that he doesn't know anything about it, so the information is still unknown. No? ^.^