Is there a relationship between stars' absolute magnitude, spectral class and relative location in a cluster? I am interested to know whether a pattern has been observed with regard to the characteristics of a star (in particular, its absolute magnitude and spectral class) and its location relative to others in the same cluster. For example, do older, cooler stars tend to occupy the centre or edges of a cluster with greater frequency than younger, hotter stars? And do stars of a certain class and magnitude tend to appear together?

I have found no specific mention of it, but the question surely relates with theories of the formation and evolution of galaxies.
Stars born together in clusters have more-or-less the same age. As a rule of thumb, any spread in age, measured in millions of years, is smaller than the extent of the cluster in parsecs.

For most stellar clusters, smaller than a few pc, the only chance of measuring age differences occurs in the first 10 million years of life. There is no evidence for age spreads in clusters beyond 30 million years old and therefore no chance of identifying any trend of age with position.

In young star forming regions, the picture is very complex. Estimating the ages of individual stars is difficult. Generally speaking, newborn stars are closely grouped together, whereas slightly older stars are a bit more dispersed. In gravitationally bound clusters, such differences tend to be eliminated in dynamical timescales of less than a few million years.

Mass segregation can occur in clusters. Some argue thus might be primordial, but it certainly can happen dynamically. The net effect is that more massive objects tend to be more centrally concentrated in a cluster.

There is evidence for multiple populations in some old globular clusters. The picture here is very complicated, still being researched, and not something that is easily summarised.