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The static and dynamic responses of Coulomb interacting particles in two-dimensional confinements are analyzed across the thermal crossover from solid- to liquid-like behaviors. While static correlations, that investigate the translational and bond orientational order in the confinements, show the footprints of hexatic-like phase at low temperatures, dynamics of the particles slow down considerably in this phase -- reminiscent of a supercooled liquid. Using density correlations, we probe long-lived heterogeneities arising from the interplay of the irregularity in the confinement and long-range Coulomb interactions. The relaxation at multiple time scales shows a stretched-exponential decay of spatial correlations in irregular traps. We propose a phenomenological model that captures much of the subtleties of our numerical simulations. Temperature dependence of the characteristic time scales, depicting the structural relaxation of the system, show striking similarities with those observed for the glassy systems, indicating that some of the key signatures of supercooled liquids emerge in confinements with lower spatial symmetries. Finally, we analyze the dynamics of particles in Coulomb clusters in terms of normal modes and demonstrate that at any given temperature, there exists a good correlation between the low-frequency normal modes and the mobile particles over the structural relaxation time. Establishing this correlation constitutes the identification of the aspect of a configuration that determines the dynamic heterogeneity of the subsequent motion. |