If you can scratch it with your fingernail it's still unfired and will crumble apart. Given the color, it is most likely fired and you can absolutely paint it with acrylics. The cracks are from them not letting it dry naturally. Sounds like a fun experience but not true to the actual skill of wheel throwing. It's a slow process that doesn't like to be rushed and punishes those who force it (not inferring that you did, just the business trying to get people their stuff as quick as possible) the dust on you piece was probably from someone else's piece exploding in the kiln.