I don't see how a roof can be "open". Does it refer to a skylight or something like that? The translation sounds really odd. This is not a criticism, I would just like to know when a roof could conceivably be "open".
Is it synonymous with στέγη?
They are but they don't have exactly the same meaning. Στέγη is a bit more general as a shelter construction while σκεπή refers to a specific type of roof, like one with wooden beams and tiles on top.