The basic answer is no, never. You can have a year of conversations without hearing or saying it, and in fact if somebdy uses it in a question I would know s/he is a beginner.
The only case where it might be said is in the phrase "The queustion is...", "השאלה היא האם", but again you can totally manage without it.
"Is" = אם
האם denotes the beginning of a question, roughly meaning "is ..." Moving the is to the beginning of the sentence
היא עצובה או שמחה -She is sad or happy (tone may indicate that it's a question)
האם היא עצובה או שמחה -Is she sad or happy
The ambiguity of the question, is the same in both languages.
Okay. I was thinking specifically of the Jewish holiday שמחת תורה, which I had been told translated to something like "the joy of Torah" or "rejoicing in the Torah," but I wouldn't be the least bit surprised if that has something to do with it being an older form of Hebrew and therefore having a slightly different meaning.
The liturgical use of שמח has different nuance than for most speech. So in liturgical context, שמח retains its Biblical connotation of rejoicing (see Deuteronomy 16:14), and has a meaning similar to celebration/celebrate/celebratory. But the liturgical lexicon has many words to describe happiness and joy and so they are nuanced in ways not common in mundane speech.
From my understanding, האם is a non-translated marker that you're asking a question. It's not necessary, and is often left out in more casual conversation, but that's its function.
If you desperately need to translate it, you might consider it as "is," but only for the sake of questions.
I should have mentioned that Duolingo’s audio is a bit flaky on my machine for some reason, so I didn’t hear the pronunciation. If we look only at the written text, then “האם” could be read either as ”הַאִם” (question word) or as “הָאֵם” (“the mother”), and either way we get a correct sentence — unless there’s some point of grammar that I’m missing.
I agree that if I had heard the pronunciation, I should have known it was “הַאִם” and not ”הָאֵם”.