Several experimental groups have reported superconductivity in single unit cell layers of FeSe on SrTiO3 and a few other substrates, with critical temperature Tc reports ranging up to 100 K, and a variety of theoretical work has been done. Here we examine more closely the interaction of a single FeSe layer with a TiO2 terminated SrTiO3(001) (STO) substrate. Several situations are analyzed: the underlying ideal interface, the effect of z-polarized longitudinal optic [LO(ẑ)] phonons in STO, electron doping of the STO substrate, substitution of Se by the bordering chalcogenides S and Te, and doping by adsorption of K on the FeSe surface. These results complement earlier studies of O and Se vacancies. The O py, py surface band of STO persists at the interface, and by sharing holes with hole pocket of FeSe it plays a part in the behavior around the interface, initially by determining the Fe Fermi level lineup with the STO bandgap. The LO(ẑ) mode causes strong band shifts around the interface but the strength of coupling to the Fe bands cannot be obtained with our methods. Adsorption of 25% K (one K per four Fe) fills the small O interface hole pocket and donates the rest of the electrons to the Fe hole pockets, filling them.