What does the "пів" part stand for in "Півдні" and "Півночі"?
Literally південь = "midday", північ = "midnight"
пів = half, mid
They really mean both :) Полудень, however, is a more common way to say "noon"
Can this на also mean to the north & south?
Yes, you would use на to speak about direction. But you need a different case (accusative): на Південь, на Північ, на Схід
Thanks Vinnfred, does this also work for в албо і у півночи? Are all those funky prepositions interchangeable?