NOT A TEACHER
I'd say that it's a noun that functions as a modifier. It's still a noun though, not an adjective. See here.
Student or Learner
A Student business initiative focusing on creative, personalized gifts, accessories & pop art decor which hopes to spread the vibrancy & playfulness that our products reflect.
I saw this statement on an advertisement board. Is "student" used as an adjective here?
(not a teacher)
Yes. It implies this business is run by students (of design or interior decoration, presumably).