Differential cross sections and hyperon polarizations have been measured for $bar{K}^0 n$, $pi^0 Lambda$, and $pi^0 Sigma^0$ production in $K^- p$ interactions at eight $K^-$ momenta between 514 and 750 MeV/$c$. The experiment detected the multiphoton final states with the Crystal Ball spectrometer using a $K^-$ beam from the Alternating Gradient Synchrotron of BNL. The results provide significantly greater precision than the existing data, allowing a detailed reexamination of the excited hyperon states in our energy range.