"The sky is clear."
'Te' + 'Iru/Imasu' defines the state of something (e.g. the sky is clear).
'Te' + 'Aru/Arimasu' defines state, due to somebody's action (and nobody is responsible for making the sky clear in our case).
Wait, so this is also different from the progressive tense ている? That would explain a few things...
No it's similar. A lot of it comes down to the fact that some English adjectives are Japanese verbs (and the opposite is true too, like and want are adjectives in Japanese but verbs in English).
Can you say そらは晴れです？Is that still correct ? Or can you only use 晴れ in reference to the weather and not a specific object?
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.