Recent data show clearly that the galaxy population at early times differed in many ways from the one we see around us today, that young galaxies were typically smaller, more irregular, more gas-rich, and more active than they are now. Birth and transfiguration are occurring throughout the wide span of cosmic history that we can now observe directly. CDM-based models are useful not only because some variant may, perhaps, turn out to be the correct theory for the growth of structure, but also because they suggest ways to characterise the dynamic processes of galaxy growth and transformation. For example, the structure they predict for the dark matter haloes of individual galaxies appears inconsistent with rotation curve data for dwarf and low surface brightness galaxies. In addition, current simulations of spiral galaxy formation in CDM-based models are unable to produce galaxies with disks as large as those observed.
Galaxy evolution is measured by comparing local and distant samples.
I think not. It is surprising, but in many ways we have better statistical data on the properties of the distant galaxy population than we do for nearby galaxies. This is quite feasible with current instrumental techniques, but it is a lot of work and unfortunately it is not seen as a glamorous enough project to feature high on most priority lists. The theoretical views on galaxy formation are largely based on large numerical simulations. As the speed delivered by computers increases, models may deliver more physics and finer resolution.