The metal-air batteries are potentially promising energy storage system that attracts due to their high theoretical energy density among other electrochemical energy storage systems. To infiltrate new barriers in the metal-air battery technology, air electrodes and its adsorption mechanisms are pre-eminent to understand the adsorption process at the atomic level. Graphene and its defects are proven as a better air electrode in the metal-air battery technology for the past few decades. Graphene can be tunable, superior compatibility with its defects and dopants, those make graphene as a potentially unique and important material to investigate. In our present study, we investigate 5-8-5, 55-77 (Stone-Waals), 555-777 and 5555-6-7777 defected sheets by functionalizing them with hydrogen around the edges and doping each defect by replacing a carbon atom with boron atom. This density functional study provides the better adsorption mechanism of CO2 and SO2 gas molecules on the defected and boron doped graphene sheets in favour of metal-air battery applications. We found that modeled sheets are favourable for the adsorption of the SO2 gas molecule with the maximum adsorption energy of - 0.343 eV, induced by 555-777 defected graphene sheet. After adsorption, it can provide proficient catalyst reactions by expanding the S-O bond length to 1.460 A. Further, we have examined the di-vacancy defects as a hydrogen storage tool and artificial photosynthesis platform. The edges are highly reactive and have shown strong binding energy with hydrogen atom. Similarly, CO2 adsorbed UV absorption graph in sheets exhibit hypsochromic effect other than 5-8-5 and B-555-777 sheets, whereas 5-8-5 and B-555-777 sheets exhibit bathochromic effect and the absorption graphs are fallen in between visible regions, which are good for photosynthesis.