Do lytter (to listen) and hører (to hear) have the same nuances as they do in English? I.e. listening is active while hearing is passive.
Yes, except when "hører" appears with the prepositions "etter" or "på".
å lytte = to listen
å høre = to hear
å høre etter = to listen (attentively), to pay attention (to what is said), to do as you're told
å høre på = to listen to (music, the radio, your parents...)
Probably because we don't form sentences that way in English. They're looking for the practical translation, not the literal one.