Ist ihnen schlecht?
Duolingo translates this as "Are they sick?" but "ihnen" shouldn't have "ist", should it? Is this a German idiomatic form?
That's because "ihnen" is not the subject of the sentence in the german version. It is the Indirect Object, that's why it is Dativ ("ihnen" instead of "sie"), it means "to/with them" not "they".
The confusing thing with this sentence is that the subject is not shown, a very uncommon situation in German. The full version would be "Ist (es) ihnen schlecht?" = "Is (something) wrong with them?"