Thinking about underground construction: could you fire individual rooms out of porcelain (or salt-fired terra-cotta, if you can somehow detoxify the fumes?) and join them together with silicone caulk/ gaskets to prevent leakage? The water table is high enough here that any hole in the ground becomes a well. For a sufficiently high budget, of course, you can just carve a chunk of granite or basalt out of a mountain, carve rooms into it, and bury it with a little bit sticking out; it will be waterproof, but that fabrication technique is costly! The question is how to get waterproof underground construction at a reasonable cost.
The traditional approach is to build things out of concrete and then pump the water from the inevitable leaks back upstairs.
You could probably use the traditional approach but seal the entire outside with tar or pitch, like an old wooden sailing ship, but that will probably only last a few decades.
If you have a conductive mesh shell around your construction, you could use it to electrolyze the groundwater to deposit minerals encasing your construction. They will preferentially deposit inside cracks that are filled with water thus sealing the cracks. This will only work if you have enough minerals dissolved in the groundwater. In a sense it’s similar to the pumping approach, in that it will fail if you have a sustained power outage, but over a much longer timescale: months or years rather than days.
Another possibility would be to seal the entire construction with some kind of flexible barrier, like latex rubber or silicone. Latex will break down spontaneously over decades and maybe biologically over years; I think silicone should be stable over a century timescale, but it is of course more expensive.
Polyethylene might be the ideal material for such a membrane, though. It’s even more chemically stable than silicone, it’s biologically stable (though less so than silicone, probably: http://www.cigre.org/var/cigre/storage/original/application/883f283abeba34bc3bdeb8caf0050c44.pdf, even though silicones can be biodegraded http://www.green-flow.co.il/Documents/Aquatain%20AMF/%D7%9E%D7%97%D7%A7%D7%A8%D7%99%D7%9D%20%D7%95%D7%A0%D7%99%D7%A1%D7%95%D7%99%20%D7%A9%D7%98%D7%97/Degradation%20of%20Silicone%20Polymers%20in%20Nature.pdf http://aem.asm.org/content/65/5/2276.full), it’s cheap as shit, it’s plastic so that it can handle subsidence without cracking, and it’s a lot stronger than silicone. If you have a 1mm LDPE or LLDPE layer in your walls, that seems like it should be plenty to keep your walls from ever leaking, at 0.94 kg/m² and €1300/tonne, that’s about €1.26/m².
This is apparently called a “geomembrane”, and it’s usually used for landfill liners to keep stuff in rather than to keep stuff out. HDPE geomembranes (actually MDPE with filler (typically carbon black) and antioxidants) ship in 6–9 meter width rolls of 1–2.5mm thickness, which are then thermally welded together onsite to form the landfill liner. Where I live, I can buy 5-meter-wide 1mm HDPE geomembrane for US$4.21/m² from some guy named Pedro Bernaldez up in Salta: http://articulo.mercadolibre.com.ar/MLA-555707538-geomembrana-polietileno-hdpe-500-de-ancho-x-1-mt-x-1000-mic-_JM
(A minimal living space of 16m³ might be something like a cylinder of 2m height and 3.19m diameter: 20.04m² of walls, 8m² of ceiling, 8m² of floor, figure really more like 10m² each of ceiling and floor what with cutting waste, total of 40m²: US$170 of geomembrane. This would involve 20 meters of seams, plus whatever’s needed to get people and air in and out.)