<p>This study explores the dynamics of a predator prey system that incorporates a specific mortality function for the predator, providing a more ecologically realistic framework. The model also features a Holling Type-II functional response modified to include the effects of additional food and prey refuge. We begin by formulating the model and analyzing its fundamental properties, such as positivity and boundedness. The existence and stability of equilibrium points are studied, followed by an investigation of codimension-one bifurcations, including transcritical and Hopf bifurcations. To capture environmental randomness, a stochastic version of the model driven by white noise is developed. Theoretical results are established for stochastic ultimate boundedness, extinction, persistence, permanence, and the existence of an ergodic stationary distribution. Numerical simulations are conducted to support both the deterministic and stochastic theoretical findings. Furthermore, a sensitivity analysis using Latin Hypercube Sampling combined with Partial Rank Correlation Coefficient (LHS PRCC) is performed to identify the most influential parameters on the system dynamics. The study offers significant insights into how predator mortality, prey refuge, and additional food interact to shape population dynamics under both deterministic and stochastic influences.</p>