In another example, I translated דקה as "moment" and it was marked wrong. Here, I said "one moment" and it was marked correct. Please explain.
Generally: minute = דקה, moment = רגע. That said - specifically in this sentence - "!דקה אחת" can be used to tell someone to wait for a short period of time, so it can be translated as "one moment!" as well.
What radagastthebrown said. minute is דקה and moment is רגע.
Still, in every language that I'm aware of "minute" and "second" are used for generic short periods of time. As in "wait a minute" or "hang on a second"
Is this by any coincidence as famous in Israel as it is in, let's say... Turkey?
I don't know about Turkey, but "דקה אחת" and "רק דקה" are phrases here and widely used.
In Israel "חצי דקה" is used all the time. (If things actually get done in half the time which is needed in Turkey, I don't know).