Translation:You may not look at another student's test.
I'm not sure what sentences you're referring to, but you usually call an elementary school student 児童 (jidou) or 小学生 (shougakusei) (生徒 seito seems to only be used in specific circumstances). 学生 (gakusei) by itself in general shouldn't be used for someone who isn't in university.
Are you sure you didn't say 小学生たち or 中学生たち? I was corrected for calling junior high school students 学生 (~2011). As a classification (for example on a form where you have to list your job), any student can be classified as 学生, but to do so in a specific school setting is unusual. See: https://chigai-allguide.com/%E5%85%90%E7%AB%A5%E3%81%A8%E7%94%9F%E5%BE%92%E3%81%A8%E5%AD%A6%E7%94%9F/
Which is why it's pointless to cling to outdated 'rules'. Can is widely used to talk about permission and dictionaries list that usage, there's nothing wrong with it whatsoever.
English students read these comments too, so this kind of thing is confusing at best and actively misleading at worst! Please don't
Per Merriam-Webster https://www.merriam-webster.com/words-at-play/when-to-use-can-and-may the use of "can" to mean "to have permission" is dated to at least the year 1500. It wasn't until the late 19th century that grammarians arbitrarily imposed a prescriptivist rule about only using "may" for permission.
It was not the year 1500. It was "by the end of the 1800s" according to the article you shared. 1500 is the year the article says they shared the senses of "ability" and "possibility," not permission.
We can debate about the level of arbitrariness with which it was originally imposed, but it is certainly not arbitrarily imposed today. My ears chafe every time I hear "can" used in the sense of permission.
According to the hints, いけません can be translated as any of "may not", "must not" or "should not". Of course, in English, these three phrases have slight differences. Which is closest to the actual meaning of いけません? Examples: May not - I am denying your request Must not - You are forbidden to do something and/or doing so would have negative consequences Should not - It is advisable not to do something
it's sort of all of the above, depending on context. usually, it means "must not" and/or "may not" as you define it, but i've heard it used in all three ways.
if you want to be clear that your intent is "should not," you can say something like "しないほうがいい" literally meaning "it's better if you don't do [that]"