A numerical study of premixed flame-turbulence interaction is performed to investigate the effects of turbulence on the structural features of the flame and the subgrid-scale (SGS) effects on vorticity dynamics, energy transfer mechanism, and turbulent transport across the flame. We consider a freely propagating methane-air turbulent premixed flame interacting with a decaying isotropic turbulence under three different initial conditions corresponding to the corrugated flamelet (CF), the thin reaction zone (TRZ), and the broken/distributed reaction zone (B/DRZ) regimes. We employ the well-established linear eddy mixing (LEM) model in large-eddy simulation (LEMLES), a new subgrid closure for reaction-diffusion occurring in the small-scales based on LEM (RRLES), and a quasi-laminar chemistry based closure in large-eddy simulation (QLLES) to simulate flame-turbulence interactions and to compare predictions with direct numerical simulation (DNS). We assess the accuracy and robustness of the closures by comparing statistical features to highlight their abilities and limitations. The newly proposed RRLES subgrid closure uses a dual-resolution grid for solving the species transport equations. Such an approach is shown to improve the existing LEMLES subgrid model especially at low Reynolds numbers. All SGS closures reveals good agreement, although there are some differences due to the closure used for convective transport of the scalar field and the reaction rate. Further analysis of the DNS dataset shows that there is a significant contribution by dilatation and baroclinic torque terms across the flame. In particular, at higher Karlovitz number, there is an abrupt change in the sign of the dilatation term, which is related to the competing effects of thermal expansion due to heat release and enhanced molecular mixing by the turbulence across the flame brush region. The enhanced mixing leads to localized pockets of cold reactants surrounded by hot products, which is only partly captured by the employed closures. The analysis of SGS kinetic energy and scalar dissipation rates indicates the presence of back-scatter of turbulent kinetic energy, and we also observe counter-gradient transport across the flame. The results suggest that further improvement of the traditional closures is needed to accurately capture the dynamics of flame-turbulence interaction.