In this theoretical work, we present the results from Density Functional Theory (DFT) calculations on novel systems formed by graphyne-gamma (GY-gamma) with defects, and Nitrogen-doped graphyne (GYN) systems. Systems with vacancy defects present a widening on the band gap. We found that the electronic properties of the GYN family may be tuned, from a semiconducting to a metallic character. This may be due to the presence of Nitrogen atoms (N) in acetylenic linkages. The N-doping was shown to generate thermodynamically stable systems with different electronic properties, which can be further confirmed by ab initio Molecular Dynamics simulations. In this work, we also analyzed the chemical stability and reactivity with the following criteria: hardness, chemical potential, and electronic density. The GYN system with defects (GYN-def) presents the lowest-energy of formation and cohesion, indicating that it may correspond to the most energetically stable system. The catalytic character of the series of graphyne systems under study was tested by assessing the capability to adsorb the O-2 molecule on the graphyne substrate. It was discovered that the GYN-beta and -delta systems represent models able to achieve O-2 molecular chemisorption onto the surface, due to the modified electronic structure after N-doping. We found activation barriers below 0.70 eV. This addresses that the process might occur spontaneously at rom temperature. Such graphyne systems represent potential candidates to be implemented as catalysis in devices such as fuel cell cathode materials.