"He is a junior high school student, but he is taller than me."
It sounds more natural to say 一个 in this context, because of the adjective 初中. If you were to say only “他是学生” it could be considered accepted. But, even in this case, it is still better to use the the measure word, rather than not using it. Other examples:
这是 一个 很漂亮的姑娘 This is a (个) very pretty girl
那是 一座 红色的楼 That is a (座) red building
这是 一只 小狗 This is a (只) puppy
Removing the measure words in these sentences is not incorrect per se, but sounds very strange, equivalent to saying "this is red building; this is puppy, this is pretty girl".
To my mind your analogy with English is invalid, as English, unlike Chinese, absolutely requires a determiner with a singular noun in these cases.
That said, I don't know what's more common. I'd be interested in hearing from a native Chinese speaker.
No, junior high school is approximately the same as middle school. A region may call it one name or the other, but usually won't have both. The upper and lower grades may vary slightly from place to place, but junior high school and middle school are both properly translated as 初中.