Photoluminescence (PL) study of pseudomorphic heavily modulation-doped AlxGa₁₋xAs/InyGa₁-yAs/GaAs heterostructures shows fundamental changes in the PL spectrum under excitation pumping and/or temperature increase. In most the high and low energy tails of the PL feature undergo the principal transformations. High-energy tail peculiarities are related to the repelling of the Fermi-edge singularity (FES) and the excitonic states. The character of repelling depends crucially on the excitation density and/or temperature. At low temperature the origination of the FES feature has been observed for the first time under increasing the excitation density. The FES appearance is accompanied by the formation of an abrupt high energy edge and occurs far below by intensity the hybridized n = 2 exciton manifestation. Strong screening of the n = 2 exciton state by photoexcited carriers is observed, resulting in the 2D electron gas-heavy hole recombination for the second electron subband. The many-body feature is detected in the magnetoluminescence spectrum. This feature develops in magnetic field B = 7 T at low temperature (T = 4.2 K) and is surely detected up to T ≈ 50 K. The LO-phonon side bands for the parent transitions between the Landau levels (LL's) are revealed in the low-energy tail of the PL spectra in magnetic field. The evolution of these phonon side-band with temperature and excitation density is observed. The enhanced strength of phonon side-bands is attributed to an enhanced Frohlich coupling with account of confined phonon and interface modes.