In this paper, systematic design and analysis of thin-film graphene-silicon solar cells with the addition of an anti-reflection coating (ARC), hexagonal boron nitride (h-BN) interlayer and decorated with Au/Ag NPs infused in rear ZnO:Al buffer layer is reported. The 3D NPs are located on the top and rear side of the solar cell. Initially, we simulated a reference 2D graphene-silicon solar cell with highest simulated short circuit current density (Jsc) 30mA/ cm2 and power conversion efficiency (PCE) of 10.65%. Using 2D and 3D full vectorial finite element method (FVFEM) simulations, we significantly improved the Jsc by 6.2mA/ cm2 from 30mA/cm2 to 36.21mA/cm2 and PCE from 10.93% to 12.03%. We utilized a patterned graphene sheet with small nanoholes to increase surface and optical conductivity. Plasmonic NPs embedded in a graphene-silicon solar cell to increase plasmonic resonance effects is investigated. The 3D position of the patterned graphene, rear buffer layer stack, size, shape, and periodicity of NPs were well-controlled and analyzed under certain parametric variation conditions. Ag NPs located inside textured ZnO:Al detached to metal contact and small periodic Au NPs decorated beneath a h-BN interlayer lead to highly efficient light confinement and increase photon current generation. The proposed device exhibits 12.03% PCE, maximum light absorption over 80% and high overall quantum efficiency (QE). Furthermore, this structure offers major light trapping advantages, including significant EM light propagation throughout the solar cell structure.