Redshift of light in dark matter Following Edwin Hubble, it is widely believed that the universe is expanding, which is based on the red-shift of light from distant objects. Can dark matter cause light to be red-shifted and make it look like the universe is expanding while in fact it is not?
 A: Dark matter does cause light to be red-shifted via gravitational redshift. The best example of this that relates to dark matter is light emitted from other galaxies (or clusters of galaxies, or any structure that is expected to he hosted in a dark matter "halo"). A photon emitted near the center of a deep gravitational potential well needs energy to "climb out" of the well; the required energy is released by a redshift of the photon. There is of course a corresponding blue-shift for a photon falling into a potential well.
A slightly more complicated example is for a photon passing through a galaxy cluster. As the photon falls into the cluster, it experiences a blueshift. Clusters are large, so it takes quite a long time (a few to tens of Myrs) for the photon to get across. During this time the cluster will typically accrete some mass, deepening its potential, so on the way out the photon will experience a redshift of a magnitude greater than the blueshift it experienced on the way in. A photon passing through a galaxy cluster therefore experiences a net redshift.
I gave these two examples because they are relevant to the second part of the question - could dark matter make the Universe appear to expand while in fact being static? The idea of an expanding Universe is indeed motivated by the observation that more distant galaxies have higher redshifts. The first example I gave doesn't scale the right way - it actually scales the other way since more massive structures form at later times, so we observe more massive structures nearby and these are the ones giving the strongest redshifts.
The second example actually does scale the right way because clusters accreted mass faster at earlier times than they do today, so the strongest redshifts from this effect will be from structures observed as they were a long time ago - those furthest away.
The reason we can't explain away cosmic expansion with all this is that the magnitude of gravitational redshift that we predict and observe in these scenarios is very small - much smaller than the redshift we attribute to cosmic expansion. Either the Universe is expanding, or something very fundamental about our understanding of gravity is flawed (my opinion is that the former is true, but people do research alternate theories of gravity; so far no breakthroughs, though).
A: Short-short version: No. Dark matter is "dark" because it does not interact electromagnetically.
A: Let us assume momentarily that your hypothesis is true. One consequence is that dark matter in different galaxies would redshift light by different amounts, in high correlation with the second distance measure given by luminosity of the baryonic matter in the galaxy. So you are back to correlating dark matter to distance, anyway. Unlikely.
A: Following Edwin Hubble, it is widely believed that the universe is expanding, which is based on the red-shift of light from distant objects. Can dark matter cause light to be red-shifted and make it look like the universe is expanding while in fact it is not?
The problem is cosmic dust can red-shift light without Universe expansion. Since cosmic dust is concentrated near the surface of galaxies, light travelling around a galaxy is most likely redshft by absorption in dust and not by gravitational attraction by dark matter. The error caused by cosmic dust can be corrected by measuring the difference in redshift between Lyman-alpha and H-alpha lines, but is never done. What this means the Universe is not expanding and dark matter does not exist. See http://www.nanoqed.org at "Cosmology by Cosmic Dust"", 2014 and "Expanding Universe or Cosmic Dust?", 2015.
