"Duo ate an orange today."
It says I should've written "多儿今天吃了一个橙", but I've never heard an orange being talked about as a 橙. Is this proper Mandarin?
It is a bit weird. People usually say 多儿今天吃了一个橙子。
I don't know who contributes to this course, but certainly some of them aren't native Mandarin speakers. It needs a lot of real-life experience to know when to use a double-syllable word.
In English, the word "orange" refers to many different variants of citrus species. The two most common variants you may come across in Chinese text is:
橘子（also commonly written as 桔子）: tangerine.
橙子: sweet orange.
Another native here, from mainland China (not Taiwan or Hong Kong). 橙 and 橙子 both sound fine to me.
橙, 橘, 柑, 桔 are four words that even the Chinese native cannot distinguish well, as they function as synonyms in many different places. If you be confused by them in the future, dictionaries are always helpful.
橘子 juzi, is the way it is normally called in Mandarin and when I was a kid teachers would correct us if we write 橙 cheng, which is Cantonese. Yet Mandarin and Cantonese have influences on each other and nowadays 橙 is also widely used. At least I hear more people say 橙汁 rather than 橘子汁 when they order an orange juice.
Um, actually it's kinda right. Orange juice is usually made from sweet orange instead of tangerine. It's just easier.
I know the issue that Cantonese-speaking areas have Mandarin courses that emphasize on weird differences between Cantonese and Mandarin that don't really exist.
I only know the fruit orange as 句子.