Influence of ordered monovacancies on elastic properties of graphene is theoretically investigated by density functional theory (DFT) calculations. Inverse linear dependence of the graphene Young's modulus on the concentration of vacancies has been revealed and migration rate of the vacancies has been calculated as a function of applied strain. It is shown that the migration rate can be controlled by applying various strains or temperatures. The influence of ordered monovacancies on magnetic properties of graphene as well as graphene-like hexagonal carbon silicide (2D-SiC) and the boron nitride (h-BN) structures is investigated. It is established that the presence of vacancies in all systems yields the appearance of local magnetic moment. However, in 2D-SiC structure the magnetic moment occurs only in the case of a Si vacancy. Influence of the distance between vacancies on the ferromagnetic or anti-ferromagnetic ordering for all structures is established.