The student profiles at Special:Student/USERNAME have a section that is supposed to list the articles being worked on by that student. However, what gets displayed (including the input box to add an article) is based on the user who is logged in, not the user whose profile is being viewed.
When a profile is viewed while logged out, no articles appear at all. If a user is logged in, viewing a profile will show what appears to be the subset of articles they are working on *for the classes in which the profiled student is enrolled*. The "Add an article" button will add articles *for the logged in user* rather than the student, but only if that user is enrolled in one of the same courses as the profiled student.
No controls (such as course deletion, or adding articles) are necessary on the student profile page, and it should simply display the articles that student is working on (and which course that article is for).
Alternatively, it might make sense to simply disable the student profile page, since it is not very useful. (Ad, do you have any objections to that?)