Using molecular dynamics simulation of a polymer glass model we investigate free-standing polymer films focusing on the in-plane shear modulus μ, defined by means of the stress-fluctuation formula, as a function of temperature T, film thickness H (tuned by means of the lateral box size L), and sampling time Δt. Various observables are seen to vary linearly with 1/H, demonstrating thus the (to leading order) linear superposition of bulk and surface properties. Confirming the time-translational invariance of our systems, μ(Δt) is shown to be numerically equivalent to a second integral over the shear-stress relaxation modulus G(t). It is thus a natural smoothing function statistically better behaved as G(t). As shown from the standard deviations δμ and δG, this is especially important for large times and for temperatures around the glass transition. μ and G are found to decrease continuously with T and a jump-singularity is not observed. Using the Einstein-Helfand relation for μ(Δt) and the successful time-temperature superposition scaling of μ(Δt) and G(t), the shear viscosity η(T) can be estimated for a broad range of temperatures.