"A student lies down on the desk."
Translation:학생이 책상에 누워요.
Using 를/을 means that the object receives the action of the verb.
저는 신문을 읽습니다. I read "what"? The newspaper
In the Duo sentence, what is lying down? It's the student not the desk. So 를/을 would mislead or confuse the reader.
에 and 에서 are both prepositions with some overlap. However, only 에 means "on".