<p>In this study, the higher finite element method (h-FEM) is employed to model and analyze the free vibration, static stability, and static bending behavior of a piezomagnetic skew-nanoplate with non-uniform thickness, incorporating flexomagnetic and surface effects. The thickness of the skew-nanoplate is assumed to vary nonlinearly along both the longitudinal and transverse directions, and the sheet is placed on a variable Pasternak elastic foundation. Based on the Kirchhoff plate theory, the nonlocal strain gradient theory, and Hamilton’s principle, the governing equations of motion are systematically derived. A four-node quadrilateral plate element with six degrees of freedom per node is developed using a Hermite-based C²-level non-conforming shape function, which demonstrates superior accuracy and rapid convergence for various geometries and boundary conditions, outperforming conventional low-order elements. The validity and accuracy of the proposed approach are verified through comparison with reliable benchmark results. Furthermore, a comprehensive parametric study is conducted to elucidate the influences of nonlocal parameter, length-scale parameter, residual surface stress, magnetic potential, elastic foundation stiffness, thickness variation profile, skew angle, geometric characteristics, and boundary conditions on the bending, stability, and vibrational responses of the piezomagnetic skew-nanoplate. This work represents a refined integration of size-dependent, surface-dependent, and flexomagnetic effects, offering valuable insight into the fundamental physics of magneto-mechanical coupling phenomena at the nanoscale.</p>