We have investigated the effect of hydrostatic pressure and temperature on phase stability of hydro-nitrogen solids using dispersion corrected density functional theory calculations. From our total energy calculations, ammonium azide (AA) is found to be the thermodynamic ground state of N4H4 compounds in preference to trans-tetrazene (TTZ), hydro-nitrogen solid-1 (HNS-1) and HNS-2 phases. We have carried out a detailed study on structure and lattice dynamics of the equilibrium phase (AA). AA undergoes a phase transition to TTZ at around ∼39-43 GPa followed by TTZ to HNS-1 at around 80-90 GPa under the studied temperature range 0-650 K. The accelerated and decelerated compression of a and c lattice constants suggest that the ambient phase of AA transforms to a tetragonal phase and then to a low symmetry structure with less anisotropy upon further compression. We have noticed that the angle made by type-II azides with the c-axis shows a rapid decrease and reaches a minimum value at 12 GPa, and thereafter increases up to 50 GPa. Softening of the shear elastic moduli is suggestive of a mechanical instability of AA under high pressure. In addition, we have also performed density functional perturbation theory calculations to obtain the vibrational spectrum of AA at ambient as well as at high pressures. Furthermore, we have made a complete assignment of all the vibrational modes which is in good agreement with the experimental observations at ambient pressure. Moreover, the calculated pressure dependent IR spectra show that the N-H stretching frequencies undergo red and blue-shifts corresponding to strengthening and weakening of hydrogen bonding, respectively, below and above 4 GPa. The intensity of the N-H asymmetric stretching mode B2u is found to diminish gradually and the weak coupling between NH4 and N3 ions makes B1u and B3u modes to degenerate with progression of pressure up to 4 GPa which causes weakening of hydrogen bonding and these effects may lead to a structural phase transition in AA around 4 GPa. Furthermore, we have also calculated the phonon dispersion curves at 0 and 6 GPa and no soft phonon mode is observed under high pressure.