If you know the apple or the man from the context already, you would translate a definite article, e.g. "An apple falls from a tree. A man eats the apple." In the first sentence, we didn't know the apple yet so we have to take the indefinite article, but after that we use "the apple". In the exercises here, you don't know the context, so you can translate it either way.
I speak a Slavic language from birth, along with English. I've also studied Russian for eight years (not bragging here, building up to the point). Nowhere in this sentence is it emphasised "a/an". Unless emphasised, you can't know if it's "the" or "a/an" (except for when there is context). Thus, I do believe that "Man eats an apple" should be okay.
Earlier in the lesson I try to answer Polish sentence to English like "A girl eats a bread" (or similar) and it was marked as wrong due to "a" particle before bread (without underscore of course). Now, in this sentence is required particle before apple. I think that there is some answers broken. I am not sure because I am not native English speaker and my mother language (Czech) does not use particles.
Sing: zna zny źnie znę zną źnie zno
Plu: źni zn znom zn znami znach źni
c is pronounced "ts", but cz is pronounced like "ch" in English which has been broken down by linguists to be "tsh" http://www.polish-dictionary.com/polish-alphabet-sounds http://www.omniglot.com/writing/polish.htm
Mężczyzna The z with the dot above it sounds more like the 's' in "measure" to me. Could someone verify that sound for us?
Indeed. "cz" is pronounced like "ch" in chimp, and "ż" like the "s" in the word "measure" , but the sound itself is harder. In general, consonants in English are more... plosive than their Polish equivalents. So English "k" sounds more like "kh" to Poles, there is more air flowing through the oral passage and the sounds are a bit more "violent" in English than in Polish.