This study explores how Navier slip boundary conditions, applied either fully or in localized hydrophobic regions, reshape the vortex–induced vibration and heat–transfer behaviour of an elastically mounted square cylinder at a Reynolds number of 22,000 and Prandtl number of the flow is 7. The coupled fluid–structure dynamics are resolved using a finite-volume solver with SST k–ω turbulence modelling and a Runge–Kutta integrator for structural motion. The fluid–structure interaction framework is validated against reference results for both stationary cylinders under slip and no-slip conditions and conventional flow-induced vibration (FIV) responses, showing excellent agreement. Simulations are performed over the reduced-velocity range of 3–14 and various slip lengths (0\le b*\le0.2). For fully hydrophobic surfaces, the cross-flow vibration amplitude is substantially reduced—by nearly 50% at Ur=10—while the inline oscillation amplitude grows markedly, reaching almost a twofold increase at Ur=12. These changes coincide with an elevation in shedding frequency and a notable weakening of lift fluctuations. Heat transfer is consistently strengthened under slip, and the mean Nusselt number reaches a maximum enhancement of approximately 53% at higher reduced velocities. When slip is introduced only on selected surfaces, its effect becomes strongly configuration-dependent. Rear-face hydrophobicity produces the greatest suppression of transverse motion, front-face slip yields the most pronounced reduction in force coefficients, and only full-surface slip results in a significant rise in heat-transfer performance. Despite local irregularities with reduced velocity, the overarching trends remain clear, with slip accelerating vortex shedding, moderating cross-flow vibrations, increasing streamwise oscillations, and enhancing convective transport. These findings demonstrate that the strategic distribution of hydrophobic regions can serve as an effective passive-control approach for improving both the dynamic and thermal behavior of square cylinders in turbulent flow.