The interaction of a proton with a deuteron is the simplest nuclear reaction. However, it allows the study of precursors of nuclear medium effects such as initial-state/final-state interactions (ISI/FSI). In case of proton knockout from deuteron induced by hard elastic pp scattering, the deviation of ISI/FSI from the ‘standard’ values may carry a signal of color transparency (CT) predicted by QCD. Another effect observed in pA reactions, known as cumulative effect, may also be potentially related to the QCD structure of the nucleus. However, any conclusions on such non-trivial QCD mechanisms from comparison with experiment depend on how accurately the usual nuclear effects are considered in the underlying reaction model. This talk will focus on the method of generalized eikonal approximation (GEA) in application to the d(p, pp)n process at relativistic energies. In case of kinematics with non-static spectator neutron, GEA provides substantial corrections to the Glauber theory. The results of numerical calculations for the nuclear transparency ratio and deuteron tensor analyzing power considering single- and double-rescattering corrections to the leading impulse approximation term will be presented both without and with CT effect. Finally, the cumulative proton production in the d(p, pp)n process will be considered taking into account single- and double-scattering graphs with intermediate nucleon and ∆-resonance. Comparison of numerical results with available data on the energy differential cross sections of cumulative proton production will be demonstrated.