Laser powder bed fusion (LPBF) has revolutionized modern manufacturing by enabling high design freedom, rapid prototyping, and tailored mechanical properties. However, optimizing process parameters remains challenging due to the trial-and-error approaches required to capture subtle parameter-microstructure relationships. This study employed a multi-physics computational framework to investigate the melting and solidification dynamics of magnesium alloy. By integrating the discrete element method for powder bed generation, finite volume method with volume of fluid for melt pool behavior, and phase-field method for microstructural evolution, the critical physical phenomena, including powder melting, molten pool flow, and directional solidification were simulated. The effects of laser power and scanning speed on temperature distribution, melt pool geometry, and dendritic morphology were systematically analyzed. It was revealed that increasing laser power expanded melt pool dimensions and promoted columnar dendritic growth, while high scanning speeds reduced melt pool stability and refined dendritic structures. Furthermore, Marangoni convection and thermal gradients governed solute redistribution, with excessive energy input risking defects such as porosity and elemental evaporation. These insights establish quantitative correlations between process parameters, thermal history, and microstructural characteristics, providing a validated roadmap for LPBF-processed magnesium alloy with tailored performance.