How do you prevent the water from damaging the property, house...
I see two possibilities: either put in a big tank, probably made of something like GRP, or pour lots of concrete. There are a number of swimming pool manufacturers who offer basement pool solutions, and I guess they've overcome these problems.
A heat-store tank needs to be sealed, because if it isn't it will lose most of its energy through evaporation. That prevents damage by damp. The only other problem is the structural one of 85 tons of water, which is not really much of an issue if the basement has a poured slab and the water is in a tank. Poured tanks might require a bit more in the way of calculations - but I wouldn't tackle this sort of a job without consulting some building professionals about the structural considerations. Anybody who can do the calculations for a swimming pool ought to be able to figure it out.
Lots of people sell basement pool solutions - eg:-
http://www.endlesspools.com/tour/basement/
Fortunately, my father-in-law and my brother are both surveyors.
...or becoming infested with nasties?
I imagine you'd put the sort of inhibitors you'd use for airconditioning, which have to prevent the growth of bugs like Legionella. The heat store is sealed anyway, though, so once the inhibitor has killed the bugs, new bugs will not be added, and any surviving bugs, stuck in the dark and without food, will not have much to live on.
My wife's qualification is in microbiology, and she doesn't see a problem with this. She sees a problem with drinking water, but that's another topic.
Also, would a house with a giant pool under it stand an earthquake?
I wouldn't know ... I don't live in earthquake country, nor yet do I intend to in the future. I guess that's one for your local structural engineer, who should be experienced in dealing with that question.