This study investigates the structural, electronic, magnetic, and pressure-dependent properties of Fe2XSi (X=Mn and Co) full-Heusler alloy through a comprehensive computational approach. The structural stability of these alloys confirmed L21 and XA prototypes as favorable structures for Fe2MnSi and Fe2CoSi, respectively. In addition, Fe2MnSi exhibits 100% spin polarization suggesting its potential suitability for spintronics applications. Conversely, Fe2CoSi does not exhibit similar behavior. The calculated magnetic moments of these alloys revealed an increase due to Coulomb interaction (U). The magnetic moments satisfy the Slater-Pauling relation, with calculated values of 3 μ_B for Fe2MnSi and 5 μ_B for Fe2CoSi. Heisenberg exchange interaction parameters are calculated to illustrate distinct magnetic interactions within the alloys. The study further explores thermomagnetic properties through Monte Carlo simulations, including thermal magnetization, thermal magnetic susceptibility, and Curie temperature (T_C). The calculated T_C were found to be 294K for Fe2MnSi and 1029K for Fe2CoSi, showing close agreement with experimental data. We additionally investigate the pressure-dependent properties of these alloys, revealing a non-linear dependence of the band gap on pressure for Fe2MnSi, with values decreasing from 0.668 eV to 0.259 eV as pressure increased from -15.917 to 23.712 GPa. For Fe2CoSi, the band gap remained zero across varying pressure conditions, indicating its metallic conducting behavior.