I think you'd have to check what "Foundation" and "The Pillars" are called in those other languages, because technically they're city districts as well. (Alternately, what the existing housing districts are called relative to the main cities.)
The
firmament is an archaic concept of the sky - a solid outer dome upon which the sun, moon and stars are attached. Now used poetically.
Alternately I'll guess that the "Blue Sky" translation might come from the Japanese term - I don't know what that is, but if I remember correctly Heavensward's Japanese title is
Azure Skies of Ishgard.
Until we've seen for sure that there will be housing, I don't think it's a good idea to assume it's coming.