It will be fine to say "the air is still". I have seen it used in a number of stories to describe exactly what you are trying to say. (Edit: if you like an example of its usage, try:" The night is cold, and the air is still. With the sound of my heart throbbing in my ears, I scanned the dark, frozen air for signs of life." I'm far from being a writer, but I hope my example helps.)

It is correct but I am not sure how the language would flow with the term 'static'. I would use frozen, or still.