Due to ample engineering and industrial applications involving electrically conducting fluids, such as in magnetic flow control devices, thermal magnetic systems, magnetic filtration and separation, and fluid transport in curved rotating channels, the present study examines the impacts of pressure-induced instability characteristics and chaotic nature of Magneto-hydrodynamic fluid flow in a rotating curved square duct (CSD), incorporating Hall and ion-slip currents. The rotational speed (Ω_T) around the vertical axis of the duct is constant while a variable transverse magnetic field is applied perpendicular to the fluid. The numerical solutions are obtained through the spectral method as a primary tool supported by additional techniques, including Chebyshev polynomial expansions and the collocation approach for the Dean number 0 < Dn ≤ 6500 over the magnetic parameter (M) 0.5 ≤ M ≤ 50.0. It demonstrates that augmenting the magnetic parameter decreases the flux value, while the Hall and ion slip currents show the opposite effect, but no significant impacts are seen on the velocity distribution. The study also shows that the bifurcation zone shifts to higher Dn and gradually weakens, while the steady curve approaches symmetry as the magnetic field is intensified. Linear stability analysis shows that the linearly stable region steadily grows as M increases, and for $M\ge 32.63$, the flow becomes linearly stable. Time evolution computations are carried out to study the unsteady behavior of the flow, and it is predicted that the multi-periodic or chaotic flow progressively transforms into a steady-state nature with the augmentation of the magnetic parameter. The transient flow experiences various instabilities, including asymmetric 2- to 4-vortex solutions.