Omega asking you that question, "What's the probability that the bead will be red" is itself information about the beads - Omega is more likely to ask that question in cases where the color is relevant.

I'm not sure what you mean by this. Obviously the color is relevant, in that it's what he wants you to guess at - but the fact that he asked about red and not about brown is not suggestive in any way. This is Omega we're talking about, not someone with normal psychology.