We perform a systematic study of binary neutron star mergers using relativistic hydrodynamical simulations with neutrinos, varying the total mass, mass ratio, and equation of state within the range of permissible values inferred from GW170817. Additionally, we conduct four long-term simulations at a fixed total mass, employing different equations of state and mass ratios. We find that asymmetric mergers systematically lead to lower dominant post-merger oscillation frequencies, larger ejecta masses, higher temperatures, and more neutron-rich outflows. By extracting the trajectories of ejected particles, we perform nucleosynthesis calculations to determine elemental yields and find a relative increase in lanthanide production in asymmetric mergers.