Re US Marshall's in Antarctica: You'all got to check this out
Re Treaties against mining- any independent colony would not be party to the treaty, and legally needn't be bound by it. The question would then be how much mining one could get away with.
Re Shelters: I was thinking more in terms of my independent small complexes, rather than one large one, except for the population center on Deception. There is no ice sheet on Deception, so that would require entirely above ground shelters, but since the weather that far north is a little more tolerable, and the geo-thermal is so easy to exploit, that may be ok. (they actually have year-round hot springs there).
As for the rest of the continent- If you are using my trench design, then your talking about one network of fishing/farming/hydronics villages along the coast, supporting another network of small mining villages in the mountains. Establishing reliable transportation between villages is challenging, but not impossible.
Space stations are the wrong model, as are undersea habitats. The problem in Antarctica isn't atmospheric pressure, it's cold, and achieving a sustainable economy.
may be more relevant. Imagine "Bio-sphere III's under the ice, providing year-round sustainable living. Not possible right away, of course, but a goal to work toward.
More realistically, at least in the early stages, each village would be more or less dedicated to a single special purpose. Each would be around 100 families or so, with Deception accommodating up to ten times as many. Each population center will have to provide it's own electrical power, as maintaining a functioning electrical grid across the continent may not be practical. Each center will have to provide it's own drinkable water, deliver it's own medical care, store the necessities for survival, and provide for it's own governance.
If it ends up becoming a country, it will be a very decentralized one. It's political culture will probably resemble Switzerland, or maybe Scandanavia. Direct democracy might be a realistic possibility. Semi-anarchist, but with a strong center to support the outlying villages.
"Would subterranean housing really work or would it just be spending more resources to heat us that way then above ground?"
If your digging into ice, a la the "covered trench" idea I mentioned earlier, then it would work quite well. Ice and snow are, somewhat counter-intuitively, excellent insulators. That's why igloos work.
“Disobedience is the true foundation of liberty. The obedient must be slaves.”