How far apart is the dust in the Sombrero Galaxy's dust lane?
Based on 1995A&amp;A...303..673E,

How far apart they are?

No idea. Somebody else might help to provide a density distribution.

Are they grouped in clumps or relatively even spaced?

This is what I really wanted to answer. They are in a concentric ring-like structure around the galaxy. The maximum optical depth is 0.8 with a mean value of 0.3. By the way, optical depth gives you a nice idea of how far apart they might be, not a good density distribution but you can get the physical picture in mind.