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That's...not quite accurate (although for current technology and space transport capabilities a reasonable explanation). Heat is exchanged by Radiation, Convection and Conduction. On Earth we use all three, in space only Radiation works so it's a lot less efficent, however while in an atmosphere...

I don't follow the logic there. How does a planet's black body radiation relate to weather or not an ecumenopoleis would work? It's not as if an ecumenopoleis would produce enough heat to matter on the scale of a planet. Not when compared to how much more is shed by increasing the planet's...

While this is true, the black body temperature of Earth is ~4 degrees below freezing. As long as you're not too close to the sun (as in mercury's orbit or such like) disposing of heat from a space station is only a problem if you don't have the ability to get large quantities of material into...

Indefinitely. If it's economic to send billions of tons of food off planet, then they can also import billions of tons of fertilizer then they can ship back billions of tons of natural fertilizer (or a fraction of that if it's desiccated). IIRC Asimov's Tarantor even had that explicitly stated...