"Unfortunately, he is not well."
Translation:Sajnos nincs jól.
"nincs" is only used for saying 'nem + van', so only for the negation of the verb "lenni" in the third singular person. Please, native speakers and advanced learners, correct me if I'm wrong.
"nincs" translating to "there's no" doesn't explain it enough. In this sentence, it means "he/she/it is not". "nem van jól" => "nincs jól"
Is there any reason that the word order is different here to another very similar sentence that's also in this lesson?
"Sajnos nem vagyok jól." as opposed to "Sajnos nem jól van."
No reason, they just want to show that the word order is free: Sajnos nem jól vagyok is OK too.
If you are so intrested in how correct is the answer, I am hungarian and I say that "nem jól van" would be better as "nincs jól". Because "nem van" is not the best collocation. :-) Just a little hint :-) EDIT: But "Sajnos nem vagyok jól." is correct as it is.