"The sky is clear."
晴れ is only for wheather. The question sentence is nore like 'the sky is clear (and will remain so)' where as 空は晴れです is more of a statement like 'as for the sky..it's clear.' I would use the question sentences if reporting the wheather to someone who doesn't know what the weather conditions are. I would use 空は晴れです if me and the listener were both outside and it's pretty clear that the sky is clear.
空が晴れです － is much like the ball is red. It tells you an aspect of what you are describing.
空が晴れています － is much like it is raining. It tells you that something is happening or ongoing.
The sky is clearing however is not quite correct. I think the best translation one could put here is something like The sky is being clear which is a rather odd sentence so the sky is clear is the better translation.
On a sidenote 【空が晴れています】 appears to be used more often.