<p>In this paper, we consider a reaction-diffusion predator–prey model with predator stage structure, nonlinear prey refuge, fear effect, maturation delay, and anti-predator behavior. First, for model without delay and diffusion, we study first verifies the solution’s positivity and boundedness, then establishes sufficient criteria for local asymptotic stability of all equilibria, and the nonlinear refuge is taken as critical parameter to discuss the Hopf bifurcation. The impact of nonlinear refuge on stability is analyzed. Next, for both diffusive and non-diffusive models, we use the delay as a critical parameter. Beyond analyzing the local stability of the positive equilibrium and detecting Hopf bifurcations, we also derive the bifurcation direction and evaluate the stability of periodic solutions via center manifold theory and normal form reduction. Furthermore, the stability conditions for the non-delayed diffusion model are determined, derive the Turing instability conditions and validate all theoretical findings through numerical simulations.</p>