We explore the effect of the number a graphene layers on the structural and dynamical properties of a free-standing polystyrene film supported by multiple graphene sheets. Detailed atomistic molecular dynamics simulations have been performed for systems with one up to four graphene sheets. Our purpose is to highlight the way that the two (PS/graphene and PS/vacuum) interfaces affect the various properties of the PS thin film as a result of the different (PS/graphene) adhesive interaction strength. Both graphene and vacuum affect the various properties of the polymer, though in a different way. Mass density profiles present an increasing maximum density peak, as the number of the graphene layers increases. Structural analysis highlights a tendency for an almost parallel to the graphene surface orientation of the phenyl rings at distances (r) very close to graphene whereas at the vacuum interface phenyl rings stick out into the vacuum phase in an almost perpendicular orientation. This behavior is similar for all four systems. On top of that clear dynamical heterogeneities due to polymer/graphene and polymer/vacuum interfaces have been observed in the level of both segmental and terminal dynamics. Four regimes for the segmental orientational dynamics of the PS chains are observed: (a) Polymer chains very close (up to similar to 0.3-0.4 nm) to the graphene layers exhibit an average segmental relaxation time about 4 orders of magnitude larger than that of the bulk system. In this region the more the graphene layers, the slower the dynamics. (b) Chains at longer distances (up to similar to 3-4 nm) show a considerable slowdown of chain dynamics with respect to the bulk PS systems. (c) A "bulk-like" regime follows (distances similar to 4.0-9.5 nm) where the chain segmental dynamics only slightly depends on r. Finally, (d) a regime (similar to 9.5-13 nm) with much faster PS chain mobility at the PS/vacuum interface appears.