We investigated the glassy dynamics of polystyrene (PS) confined in anodic aluminum oxide (AAO) nanopores by differential scanning calorimetry. Based on the outcome of our experiments, we show that the cooling rate applied to process the 2D confined PS melt has a significant impact on both the glass transition and the structural relaxation in the glassy state. A single glass transition temperature (Tg) is observed in quenched samples, while slow-cooled PS chains show two Tgs corresponding to a core-shell structure. The former phenomenon resembles what is observed in freestanding structures, while the latter is imputed to the adsorption of PS onto AAO walls. A more complex picture was drawn for physical aging. In the case of quenched samples, we observed a non-monotonic trend of the apparent aging rate that in 400 nm pores, reaches a value almost twice as larger than what is measured in bulk and decreases upon further confinement in smaller nanopores. For slow-cooled samples, by adequately varying the aging conditions, we were able to control the equilibration kinetics and either separate the two aging processes or induce an intermediate aging regime. We propose a possible explanation of these findings in terms of distribution in free volume and the presence of different aging mechanisms.