Using density-functional theory (DFT) band-structure calculations, we study the crystal structure, lattice dynamics, and magnetic interactions in the Shastry-Sutherland magnet SrCu2(BO3)(2) under pressure, concentrating on experimentally relevant pressures up to 4 GPa. We first check that a ferromagnetic spin alignment shortens the nearest-neighbor Cu-Cu distance and reduces the Cu-O-Cu angle compared to the state with the antiferromagnetic spin alignment in the dimers, in qualitative agreement with the structural changes observed at ambient pressure as a function of temperature and applied field. Next, we determine the optimal crystal structures corresponding to the magnetic structures consistent with, respectively, the dimer phase realized at ambient pressure, the Neel ordered phase realized at high pressure, and two candidates for the intermediate phase with two types of dimers and different stackings. For each phase, we performed a systematic study as a function of pressure, and we determined the exchange interactions and the frequencies of several experimentally relevant phonon modes. In the dimer phase, the ratio of the inter- to intradimer couplings is found to increase with pressure, in qualitative agreement with various experiments. This increase is mostly due to the decrease of the intradimer coupling due to the reduction of the Cu-O-Cu angle under pressure. The phonon frequency of the pantograph mode is also found to increase with pressure, in qualitative agreement with recent Raman experiments. In the Neel phase, the frequency of the pantograph mode is larger than the extrapolated value from the dimer phase, again in agreement with the experimental results, and accordingly the intradimer coupling is smaller than the extrapolated value from the dimer phase. Finally, all tendencies inside the candidate intermediate phases are thoroughly worked out, including specific predictions for some Raman active phonon modes that could be used to pin down the nature of the intermediate phase.