Motivated by the successful synthesis of the porous graphitic carbon nitride (C6N7) monolayer very recently, we investigate the structural and electronic properties of C6N7 with doped and embedded with various atoms by means of spin-polarized density functional theory calculations. C6N7 monolayers doped with B, N, C, and O atoms have been revealed as stable and predicted to be feasible for experimental fabrication as free-standing monolayers based on the energy and thermal stability. Our computations demonstrate that while the C6N7 is a semiconductor, the doped C6N7 monolayers can be metal, dilute-magnetic semiconductor or half-metal. Further, a non magnetic moment is discovered in three of the doped C6N7 models and their electronic properties are disclosed to depend strongly on the spin configurations. The electronic properties of C6N7 depend on the doping atoms and doping sites. Furthermore, the effect of embedding of common nonmetal atoms such as B, C, N, S, O, Al, Si and P as well as transition metal including Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Cu and Zn atoms on the electronic and magnetic behavior of the C6N7 are studied. The charge transfer analysis shows that all embedded atoms act as electron donors, expect N, O and S atoms which act as electron acceptors when interacting with C6N7. The modification of the electronic band structure of C6N7 as the underlying mechanism for the changes in its electronic properties has been investigated. The intention is to demonstrate how entering the above mentioned impurities changes the nature of C6N7 into a metal, ferromagnetic-metal or dilute-magnetic semiconductor. These findings give not only an insight into the physical properties of doped and embedded C6N7 monolayer by different atoms, but also can serve as a guide to discover future possible applications of this novel material.