Electromagnetic fields of the simplest time-dependent sources (current loop, electric dipole, toroidal solenoid, etc), their interactions with an external electromagnetic field and between themselves are found. They are applied to the analysis of the Lorentz and Feld-Tai lemmas (or reciprocity-like theorems) having numerous applications in electrodynamics, optics, radiophysics, electronics, etc. It is demonstrated that these lemmas are valid for more general time dependences of the electromagnetic field sources than it was suggested up to now. It is shown also that the validity of reciprocity-like theorems is intimately related to the equality of electromagnetic action and reaction: both of them are fulfilled or violated under the same conditions. Conditions are stated under which reciprocity-like theorems can he violated. A concrete example of their violation is presented.