I said "She is departing" and I cannot see why this would be incorrect. I know this is different from leaving but I don't see why saying departing (like from her house or workplace) would be different from the sentence. Does anybody know ?
No, not just to leave for the day. You are correct, it's a weird thing to say. In this context (when it's used as a synonym for leaving/exiting) - it's used for journeys, or vehicles (I.e. The train is departing from the station), or poetically.
Everything you have said is correct. What's odd is that DL gave "is departing" as one of the drop down clues. Then they marked it wrong. I flagged it. As long as there is no context, they should accept other correct translations.