The course appears to be organized and everything is introduced very clearly in the tips and notes. Do "dobrý" and "den" mean different things on their own, or is it just one word in two parts, sort of like the English "By the way" - each of the words in it is a different word, but the whole thing translates differently?
It is exactly like the English "Good morning" or "Good afternoon", as "dobrý" = "good" and "den" = "day" (which covers both "morning" AND "afternoon"). The same applies for German "Guten Tag".
Yes, like добрый день (dóbryj denʹ) in Russian and similarly in many other languages.
But it seems to mean "good day" and can be used, apparently, either in the morning or afternoon. So why say it means "good morning" when it really means "good day"?
"Good day" is not very common in English (apart from the Australian g'day) but I think it really would be better to translate it literally. But I think that for example the Spanish and the Portuguese Duolingo courses also translate "buenos dias" and "bom dia" as "good morning".