In preparation for high fusion plasma performance operation of the newly operating spherical tokamak MAST-U, the equilibrium and stability properties of plasmas in the MAST database, as well as projections for MAST-U, are explored. The disruption event characterization and forecasting (DECAF) code is utilized to map disruptions in MAST, particularly with regard to vertical displacement events. Loss of vertical stability control was not found to be common in MAST, providing reassurance for MAST-U operation. MAST equilibria were reconstructed with magnetic diagnostics only, adding kinetic diagnostics, or finally also adding magnetic pitch angle data. The reconstructions work well for MAST and the procedures are set up for MAST-U, including determination of the plasma current in the first MAST-U discharges. A 3D wall model of MAST-U has been constructed in the VALEN code, indicating that significant toroidal currents may be induced in the conducting structure. Rotation measurements may also be included in the reconstructions, and a test with the FLOW code of a rotating MAST plasma indicates a small shift of the pressure contours off of the magnetic flux surfaces may be expected. Unstable resistive wall modes (RWMs) may constrain the performance of high pressure MAST-U plasmas. A machine learning (ML) assisted algorithm for stability calculation developed for the NSTX spherical tokamak has been applied to MAST plasmas. Improvements and expansion of the ML techniques continue, including semi-supervised learning techniques and a detection algorithm for unstable RWMs. Finally, projections of MAST-U plasma stability have been performed, indicating that a region of high pressure operational space exists in which the new passive stabilization plates act to stabilize ideal kink modes, and RWMs may be stabilized by kinetic effects or active control.