  The investigations of the spectral and dynamical delocalization-localization
(DL) transition have revealed intriguing features in a wide range of
non-Hermitian systems. The present study aims at exploring the spectral and
dynamical properties in a non-Hermitian quasiperiodic system with asymmetric
hopping in the presence of Rashba Spin-Orbit (RSO) interaction. In particular,
in such systems, we have identified that the DL transition is associated with a
concurrent change in the energy spectrum, where the eigenstates always break
the time-reversal symmetry for all strenghts of the quasiperiodic potential,
contrary to the systems without RSO interaction. Remarkably, we find that the
reality of energy spectrum under the open boundary condition that is frequently
symbolised as a hallmark of the skin-effect, is a system-size dependent
phenomena, and appears even when the associated energies are indeed complex. In
addition, it is demonstrated that the spin-flip term in the RSO interaction in
fact possesses a tendency to diminish the directionality of the skin-effect. On
scrutinizing the dynamical attributes in our non-Hermitian system, we unveil
that in spite of the fact that the spectral DL transition accords with the
dynamical phase transition, interestingly, the system comes across
hyper-diffusive and negative diffusion dynamical regimes depending upon the
strength of the RSO interaction, in the spectrally localized regime.
