Complex multi-phase phenomena, including turbulent flow, solidification, and magnetohydrodynamics (MHD) forces, occur during the continuous casting (CC) under the applied electromagnetic brake (EMBr). The results of the small-scale experiment of the liquid metal model for continuous casting (mini-LIMMCAST) at the Helmholtz-Zentrum Dresden-Rossendorf (HZDR), investigating MHD flow with a deep immersion depth of 100 mm, are supplemented by newly presented numerical studies with the shallow position of the submerged entry nozzle (SEN) at 50 mm below the meniscus. Herein, the focus is on the MHD effects at the meniscus level considering (i) a fully insulating domain boundary, (ii) a perfectly conductive mold, or (iii) the presence of the solid shell. The volume-of-fluid (VOF) approach is utilized to model a Galinstan flow, including free surface behavior. A multiphase solver is developed using conservative MHD formulations in the framework of the open-source computational fluid dynamics (CFD) package OpenFOAM®. The wall-adapting local eddy-viscosity (WALE) subgrid-scale (SGS) model is employed to model the turbulent effects on the free surface flow. We found that, for the deep immersion depth, the meniscus remains calm under the EMBr for the conductive and semi-conductive domain. For the insulated mold disregarding the SEN position, the self-inducing MHD vortices, aligned with the magnetic field, cause strong waving of the meniscus and air bubble entrapment for shallow immersion depth. Secondary MHD structures can form close to the meniscus under specific conditions. The influence of the EMBr and immersion depth on the flow energy characteristics is analyzed using power spectral density (PSD).