Stellar multiplicity is correlated with many stellar properties, yet multiplicity measurements have proven difficult for the M dwarfs—the most common type of star in our galaxy—due to their faintness and the fact that a reasonably complete inventory of later M dwarfs did not exist until recently. We have therefore carried out the Pervasive Overview of "Kompanions" of Every M dwarf in Our Neighborhood (POKEMON) survey, which made use of the Differential Speckle Survey Instrument on the 4.3 m Lowell Discovery Telescope, along with the NN-EXPLORE Exoplanet Stellar Speckle Imager on the 3.5 m WIYN telescope. The POKEMON sample is volume limited from M0V through M9V out to 15 pc, with additional brighter targets at larger distances. In total, 1125 targets were observed. New discoveries were presented in the first paper in the series. In this second paper in the series, we present all detected companions, gauge our astrometric and photometric precision, and compare our filtered and filterless speckle observations. We find that the majority (58.9%) of the companions we detect in our speckle images are not resolved in Gaia, demonstrating the need for high-resolution imaging in addition to long-term astrometric monitoring. Additionally, we find that the majority (73.2%) of simulated stellar companions would be detectable by our speckle observations. Specifically within 100 au, we find that 70.3% of simulated companions are recovered. Finally, we discuss future directions of the POKEMON survey.