I translated this as: "He reads literature at school."
I know that in Turkish one "reads" a subject at a university, rather than "studies" a subject, as we say in English. But does that mean my translation is necessarily wrong? For instance, one mother might tell another mother that she can't get her son to read literature at home but that he reads it at school.
No, this sentence would always be understood as studying.
We don't say "edebiyat okumak" to mean "to read literature". We'd say "edebi eserler okumak" maybe, (to read literary works).
In a specific context "okulda edebiyat (dersi) çalışıyor" is possible. In case the English sentence has "the" such as "he is reading the literature" this may be translated as "literatürü okuyor". But this is a literature on a certain especially scientific area like medical literature etc.