Bah. That's a hard one. B is definitely wrong, but I'd have no problem using A OR C. I'd say to go with C, though. An "expansion" is more indicative of actual moveable area than an "extension" is, so it's more right than A is.

No, not clearly wrong. "Extension" concrete while "expansion" is abstract. You can only physically build an extension.

The dilemma is that 'extension' is a building term. It is jargon for this part of a building added later. 'Addition' could also be used. Of course, expansion sounds appropriate, but the building industry has been using extension.