We investigate the thermodynamic and dynamic properties of a model unentangled glass-forming polymer melt over a wide range of pressures (P) and temperatures (T) using molecular dynamics simulation. We show that the T dependence of the reduced thermal expansion coefficient and isothermal compressibility becomes weaker for higher P. Based on the generalized entropy theory, these trends suggest that the isobaric fragility of glass formation decreases with increasing P, consistent with our analysis from the structural relaxation time (tau(alpha)). Moreover, we confirm previous findings that the onset and end of the glass formation process in our model can be estimated solely based on the static structure factor. We then provide a detailed analysis for the T and P dependence of tau(alpha) as well as other quantities characterizing the dynamic heterogeneity of glass forming liquids. In particular, we discuss how T and P influence the average extent L of the stringlike cooperative motion of monomers in our model polymer melt, an important molecular-scale quantity in the string model of glass formation in which the activation free energy increases from its high T value by a factor determined by L. Our work thus offers molecular insight into the strong influence of P on the dynamics of glass-forming liquids, in addition to providing observational data that are crucial for developing improved theories of glass formation.