Well, if the dark matter is ~90% of the mass of everything, that doesn't necessarily mean that 90% of the mass of every thing is dark matter. As far as I understand it, we see the effects of the large amount of extra matter but we don't really know where it is or how it's distributed. That could mean that there isn't any dark matter clustered in large enough quantities close by for us to detect.

Assuming it's not near us, why would that be? Our star isn't much affected by it. We can't see nearby stars being pulled willy-nilly.

Well, a really spread out distribution across the universe would explain that.

And if it's a weird non-localised 'blanket' that can't hit you in the foot, then it'd be great to have some guesses as to the structure so we can test for it.

Well we have a prediction for what the particle would look like (/act like). That's what the detector is there for. Well, not just dark matter. Think neutrinos and Cherenkov radiation.

As far as the other questions go, I'm not sure enough to answer and I'm pretty sure that some of those questions are open.