We conduct a comprehensive investigation of the detectability of the first stars and their enrichment signatures in galaxy clusters. We show that the mean metallicity of outflows from objects containing these Population III (PopIII) stars is well above the critical transition metallicity (Z_cr \sim 10^-4) that marks the formation of normal stars. Thus the fraction of PopIII objects formed as a function of redshift is heavily dependent on the distribution of metals and fairly independent of the precise value of Z_cr. Using an analytical model of inhomogenous structure formation, we study the evolution of PopIII objects as a function of the star formation efficiency, IMF, and efficiency of outflow generation. For all models, PopIII objects tend to be in the 10^6.5-10^7.0 solar mass range, just large enough to cool within a Hubble time, but small enough that they are not clustered near areas of previous star formation. Although the mean metallicity exceeds Z_cr at a redshift of 15 in all models, the peak of PopIII star formation occurs at z \sim 10, and such stars continue to form well into the observable range. We discuss the observational properties of these objects, some of which may have already been detected in ongoing surveys of high-redshift Lyman-alpha emitters. Finally, we combine our PopIII distributions with the yield models of Heger and Woosley (2002) to study their impact on the intracluster medium (ICM) in galaxy clusters. We find that PopIII stars can contribute no more than 20% of the iron observed in the ICM, although their peculiar elemental yields help to reconcile theoretical models with the observed Fe and Si/Fe abundances. However, these stars tend to overproduce S/Fe and their associated SN heating falls far short of the observed level of 1 keV per ICM gas particle.

24 pages, 14 figures, Accepted for Publication in ApJ