Research Challenge 1: The main reason that the Hubble diagram in Explore 7 looks so unclear is that the assumption you made back at the beginning - that all galaxies have similar properties - was false. In reality, galaxies vary greatly - some are big and bright, some are small and faint. So if you see a big bright galaxy next to a small faint galaxy, it might be true that the galaxies are at the *same* distance, but one really is bright and one really is faint. You can't assume that just because a galaxy looks bright that it must be close to us.
One way around this problem of galaxy variations is to look at galaxy clusters like the one shown to the right. You can assume that all galaxies in a cluster are about the same distance away from us, so any differences in brightness are due to the galaxies' variation. If you compare the brightest (or biggest, or 10th brightest, or 10th biggest, etc.) galaxies in one cluster to the biggest (etc.) in another cluster, then any differences of magnitude must be due to the difference in distance between two clusters.
Look at SkyServer's Famous Places page for the Abell Galaxy Clusters (click on the blue link). Look at each cluster one by one in the Navigation tool (click on each picture to launch the tool). You will probably have to zoom out one or two steps to see the whole cluster.
Click on each galaxy you think is part of the cluster. Save each galaxy in your Notebook and record its g magnitude. Click the "specObj" checkbox. Click on one of the galaxies in the red squares, and click the "Explore" link in the right-hand frame. A new window will open. Look at the value "z" just above the spectrum (wavy line) near the bottom of the page. This z value is the redshift of the galaxy (and, by extension, the entire cluster).
Compare the g magnitude of the brightest galaxy (or some other measure of distance) to the redshift of each cluster. You should now have 2 columns (distance and redshift) for six data points (one for each Abell cluster).
Make a Hubble diagram for the six Abell galaxy clusters. How does the diagram compare to the ones you made in Explore 4/5 and 7? Why is this diagram more believable? If you want to add more points to the diagram, look up the coordinates of the other Abell clusters by clicking the "Abell data" link at the bottom of the Abell clusters page.