"Aren't they listening?"
Translation:Ils n'écoutent pas ?
"Écoutant" is a present participle. It also means "listening," but it can't be used in this context. You must use the present tense verb, "écoutent."
However, here are some sentences where écoutant can be used.
Je mange en écoutant à la radio. = I'm eating while listening to the radio.
En écoutant leur maîtresse, les élèves ont appris leur leçon. = By listening to their teacher, the students learned their lesson.
Here is a helpful link explaining present participles/gerunds in French. https://www.lawlessfrench.com/grammar/present-participle/
To me, "Ils n'écoutent pas" should not be a question. The sentence sounds like "they are not listening." Or could it be that the question mark makes all the difference - that is, with the question mark the meaning becomes, "Aren't they listening ?" and without the question mark, the meaning is, "They are not listening." Can someone please confirm what I am saying or correct me?
Yes, just as in English, we can change a statement into a question by adding a question mark. The same thing is done orally with a voice inflection at the end of the phrase.
For example :
Tu manges de la viande. = statement (You eat meat.)
Tu manges de la viande ? = question (You eat meat?/Do you eat meat?)
Here is a great link on the various ways to ask a question in French: https://www.thoughtco.com/questions-in-french-1368935
I believe the proper answer is N'écoutent ils pas. Are they not listening?
Isn't there a clear distinction between to listen (entendre) and to hear (écouter) ? c.f. 'look' and 'see'
Yes. As in English there is a difference between listening "écouter" and hearing "entendre".
Hearing is more of a passive activity, and in English the verb is stative. J'entends un oiseau. → I hear a bird.
Listening is active. J'écoute la musique. → I am listening to music.