"Duo ate an orange today."
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.
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.
The difference depends on what part of China you're from, really. The further south you are, the more likely you are to say 橙子 instead of 橘子. My family is from Shanghai for example, and we say 橙子 much more often than we say 橘子. It's a regional difference in vocabulary that has its roots in which Chinese language was originally spoken in the city that Mandarin was introduced to. In Wu speaking areas, it's 橙子, same for Cantonese and I'd wager Hakka & Hokkien speaking areas as well.
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.