Recently, an atomic-scale two-dimensional silicon carbide monolayer has been synthesized [Polley et al., Phys. Rev. Lett. 130, 076203 (2023)], which opens up new possibilities for developing next-generation electronic and optoelectronic devices. Our study predicts the pristine SiC monolayer to have an "indirect" band gap of 3.38 eV (K M) and a "direct" band gap of 3.43 eV (K K) calculated using the HSE06 functional. We performed a detailed investigation of the various possible defects (i.e., vacancies, foreign impurities, antisites, and their various combinations) on the structural stability, electronic, and optical properties of the SiC monolayer using a first-principles-based density-functional theory (DFT) and molecular dynamics (MD) simulations. A number of physical quantities, such as the formation energy, electronic band gap, and the effective masses of charge carriers, have been calculated. We report that the SiC monolayer has a very low formation energy of 0.57 eV and can be stabilized on TaC{111} film by performing the surface slab energy and interfacial adhesion energy calculations. Nitrogen doping is predicted to be the most favorable defect in silicon carbide monolayer due to its very low formation energy, indicating high thermodynamic stability. The analysis of the electronic band structure and the density of states shows that the additional impurity states are generated within the forbidden region in the presence of defects, leading to a significant reduction in the band gap. An interesting transition from semiconducting to metallic state is observed for NC and AlSi defective systems. For the pristine SiC monolayer, we find that the conduction band is nearly flat in the M K direction, leading to a high effective mass of 3.48mo. A significant redshift in the absorption edge, as well as the occurrence of additional absorption peaks due to the defects, have been observed in the lower energy range of the spectrum. The calculated absorption spectra span over the visible and ultraviolet regions in the presence of defects, indicating that the defective SiC monolayers can have potential optoelectronic applications in the UV-visible region.