We present the results of experimental and theoretical studies of the surface plasmon polariton excitations in heavily doped GaN epitaxial layers. Reflection and emission of radiation in the frequency range of 2-20 THz including the Reststrahlen band were investigated for samples with grating etched on the sample surface, as well as for samples with flat surface. The reflectivity spectrum for p-polarized radiation measured for the sample with the surface-relief grating demonstrates a set of resonances associated with excitations of different surface plasmon polariton modes. Spectral peculiarities due to the diffraction effect have been also revealed. The characteristic features of the reflectivity spectrum, namely, frequencies, amplitudes, and widths of the resonance dips, are well described theoretically by a modified technique of rigorous coupled-wave analysis of Maxwell equations. The emissivity spectra of the samples were measured under epilayer temperature modulation by pulsed electric field. The emissivity spectrum of the sample with surface-relief grating shows emission peaks in the frequency ranges corresponding to the decay of the surface plasmon polariton modes. Theoretical analysis based on the blackbody-like radiation theory well describes the main peculiarities of the observed THz emission.