How do those instruments work at all?

These questions would be better asked in the "science" forum (and probably are answered there). But just for short:

1. Whatever is far enough outside the frequency spectrum we try to observe is indeed filtered out by design (suspension etc). However there is enough disturbance or "noise" remaining in the data that is recorded that we need that enormous computing power of Einstein@Home to filter out what might really be gravitational waves.

2. The mirrors are indeed very "flat". I didn't attend the "coating" sessions of the conferences, but for every tiny aspect of the experiment there are quite some people spending a lot of effort on it.

BM