well, the watch doesn't actually work (though when it did, it was waterproof, and in spite of the seals having disintegrated markedly, water doesn't seep in too much - oh, it's a mechanical watch, kind of an odd mechanism, old). It's the most valuable thing she owns, so she tends to not take it off much.
well, the 'stumps' as you say are structural elements of the under-structure of the lands, actually (it has to do with the concept of stratification of a city over very long periods of time, specifically height reduction and full coverage atmospheric conditions required for a very long time, but that's gliding over the conditions the story takes place in). impervious pools like this (which is a pretty large water area) can sometimes be unstable, but the settling of the under-structure here is known to be relatively stable, so it's not unsafe really (though there are three points in the 'lake' where water takes routes down into the substructure.
If none of that makes sense, don't worry about it too much
If some of it did, think about how running water works in relation to large glaciers.
and i'll shut up now