południu is very similar to the word południe, which means both the south, and the noon, as conor.raff pointed out. Is that perhaps because the sun is somewhat in the south during noon?
"Południu" is locative form of "Południe"= noon/South
Yes. To me as a native Polish person, those concepts are inherently the same.
Wschód(East) is where słońce wschodzi (sun rises)
Zachód (West) is where słońce zachodzi (sun sets)
Południe (South) is where sun is at południe (noon)
I imagine północ (North) as a direction where sun never is , but I guess you can also imagine sun going full circle - half at day (above), and half at night (below), and północ=North is where in this imaginary journey sun would be in the middle of the night. (midnight=północ)
The idea is similar in Hebrew. The word for North (צפון) means "hidden", where the sun never is.
No. "czas" is masculine, but not-animate, so in Accusative it looks the same as in Nominative: "czas".
Would the translation, "I have time after noon," meaning literally, "My schedule clears up after 12 PM," be acceptable?
Well... yes. Added now.
I'd rather specify it saying "po dwunastej" (after 12) instead of "po południu", but that sure is a correct interpretation.
No, either you say it in the morning, or you set a meeting or something and say you have time in the afternoon that day, or that you usually have time in the afternoon.
In English it would be idiomatic to say "I'm free in the afternoon" or "I'm free this afternoon" - would these be correct translations for this sentence?