Honestly, that is a somewhat watered down assessment. Most of those entities you described are faeries, or otherwise part of the Fair Folk mythology, making the idea that all faeries are related to the element of air somewhat off. The Fair Folk in general are party to a wide range of elements, as one might discover in the way that you connected several of them to specific, different, elements. And those who practice dragon magic would likely be quick to point out that dragons often favor a wide range of elements, and may not even choose one to favor in particular.
As previously suggested (oh how I wish people would read AND comprehend) elementals are spirits that appear to us in these various forms. But the friendship part? You're spot on with that.