  X-ray diffraction pressure studies at room temperature demonstrate that the
spinel FeAl$_{2}$O$_{4}$ transforms to a tetragonal phase at ~18 GPa. This
tetragonal phase has a highly irregular unit-cell volume versus pressure
dependence up to ~45 GPa, after which a transformation to a Cmcm post-spinel
phase is onset. This is attributable to pressure driven Fe-Al site inversion at
room temperature, corroborated by signatures in the 57Fe M\"ossbauer
spectroscopy pressure data. At the tetragonal to post-spinel transition, onset
in the range 45-50 GPa, there is a concurrent emergence of a non-magnetic
spectral component in the M\"ossbauer data at variable cryogenic temperatures.
This is interpreted as spin crossover at sixfold coordinated Fe locations
emanated from site inversion. Spin crossover commences at the end of the
pressure range of the tetragonal phase and progresses in the post-spinel
structure. There is also a much steeper volume change dV/V ~ 10% in the range
45-50 GPa compared to the preceding pressure regime, from the combined effects
of the structural transition and spin crossover electronic change. At the
highest pressure attained, ~106 GPa, the M\"ossbauer data evidences a
diamagnetic Fe low-spin abundance of ~50%. The rest of the high-spin Fe in
eightfold coordinated sites continue to experience a relatively small internal
magnetic field of ~33 T. This is indicative of a magnetic ground state
associated with strong covalency, as well as substantive disorder from site
inversion and the mixed spin-state configuration. Intriguingly magnetism
survives in such a spin-diluted post-spinel lattice at high densities. The
R(300 K) data decreases by only two orders of magnitude from ambient pressure
to the vicinity of ~100 GPa. Despite a ~26% unit-cell volume densification from
the lattice compressibility, structural transitions and spin crossover.
