Continuous casting of steel in an industrial billet caster is modeled numerically including multiphase turbulent flow, mold electromagnetic stirring (M-EMS), heat transfer, and solidification. Two different steel grades (case-hardening and micro-alloyed steel) and casting powders are considered in the study to evaluate the castability and powder performance. Existing models to estimate thermophysical properties of casting powders are reviewed and compared to measurement data. Complex mold taper design is considered by constructing a digital twin and applying a corresponding velocity for the solidified shell in 3D. Slag infiltration is simulated from the beginning of casting to steady operation as a function of shell solidification and resulting heat transfer between liquid steel and oscillating mold wall. Additionally, the model predicts air gap size, excessive taper, and mold friction through a quasi-thermomechanical analysis. This includes a new approach to estimate mold friction based on Lubrication Index (LI) and Contact Index (CI) concepts. The resulting shell thickness, cooling water temperature, nail-dipping measurement, and mold friction are compared to plant data and literature for validation. This novel modeling approach can address phenomena difficult to analyze on real casters such as slag entrainment and infiltration, corresponding thermal response, and contact conditions between shell, slag, and mold.