Actually, 'bleiben Sie bitte in der Leitung' is the right way to say 'please hold the line' / '…stay on the phone' in German: http://www.duden.de/rechtschreibung/Leitung#Bedeutung3c
In English you can say "Please remain on the line". I think it is the same thing, even though you are not ON the line in English, IN makes more sense. I also used leadership and had no idea what it meant. The translation is missing? But I am not sure if we can translate it as a "LINE"...
Since I thought the sentence meant "Please stay in the line" (the queue), I decided to test Duo's understanding of English by omitting "the" and writing the more common expression: "Please stay in line." Duo corrected this to "Please stay in the line." That seemed oddly inflexible.
Good thing I came to the discussion! Duo's correction is a mistake and will mislead students who don't realize that the line referred to is a telephone line. The correction should be "Please stay on the line." Unfortunately, it's not possible to report this problem. But thank Duo for discussions!
I don't think this is necessary. May be regional. All my lookups led to "in der Leitung", e.g. https://www.dict.cc/?s=in+der+Leitung and there are far more hits for this: https://context.reverso.net/%C3%BCbersetzung/deutsch-englisch/in+der+Leitung+bleiben
Yes. It's a very common way of saying it. E.g. here's a book that uses the phrase as its title: https://www.amazon.de/Please-Stay-Line-Dangerous-American/dp/1499797516.