This study investigates transformer performance by combining Finite Element Method (FEM) and MATLAB/Simulink modeling and simulations, focusing on efficiency, core losses, and ferroresonance phenomena. Analyzing transformer behaviors, including anisotropy and non-linearity, via FEM simulations and analytical formulations reveals significant insights. Grounded in the Nonlinear Inductance Electromagnetic Transformer (NIEMT) Model and Maxwell's equations, the study models core losses, reluctivity, and relative permeability to capture magnetic flux dynamics. MATLAB/Simulink models simulate ferroresonance effects on distribution transformer behavior in low voltage power systems. Findings highlight differences in ferroresonance resilience: Total Harmonic Distortion (THD) in the baseline transformer is up to 30% higher than in the optimized transformer. Additionally, respective flux density and losses are 40% and 2.55% higher in the baseline compared to the optimized transformer, demonstrating how design changes enhance performance. Experimental validation underscores practical implications, while ferroresonance analysis identifies stability challenges and mitigation strategies. This research offers valuable insights for transformer design and power system stability enhancement.