我们下星期五会有英语考试。

I have a question about this bit "下星期五". Shouldn't it be 下个星期五, as we usually see elsewhere (下个月, 下个星期 )? The funny thing is that this lesson here: https://www.duolingo.com/comment/8626265/Mandarin-Chinese-Lesson-4 also uses the classifier: "You can express things like "last Monday" (上个星期一) or "next Friday" (下个星期五) the same way."

This sentence can be better expressed as: "We have an English test next Friday." This removes the need for "will" because the time (referencing the future) is specified.

So this is fine: 我们下星期五有英语考试。