It would have to be a gentle spray.
-
Seriously, though... I think the applications in terms of insulation are tremendous for the aerogel... that's assuming the milk protein doesn't break down too easily.
-
The space elevator would have to have multiple lifts going up and down. And yes, beaming power to the nano-assemblers would be an issue. A lot of fictional nanoassemblers get a free pass with some unspecified form of endless energy coming from out of the authors' arses... but in real life, we'll need to feed them with something to keep them going.