The Kepler light curves used to detect thousands of planetary candidates are susceptible to dilution due to blending with previously unknown nearby stars. With the automated laser adaptive optics instrument, Robo-AO, we have observed 620 nearby stars around 3857 planetary candidates host stars. Many of the nearby stars, however, are not bound to the KOI. We use galactic stellar models and the observed stellar density to estimate the number and properties of unbound stars. We estimate the spectral type and distance to 145 KOIs with nearby stars using multi-band observations from Robo-AO and Keck-AO. Most stars within 1" of a Kepler planetary candidate are likely bound, in agreement with past studies. We use likely bound stars and the precise stellar parameters from the California Kepler Survey to search for correlations between stellar binarity and planetary properties. No significant difference between the binarity fraction of single and multiple-planet systems is found, and planet hosting stars follow similar binarity trends as field stars, many of which likely host their own non-aligned planets. We find that hot Jupiters are ~4x more likely than other planets to reside in a binary star system. We correct the radius estimates of the planet candidates in characterized systems and find that for likely bound systems, the estimated planetary radii will increase on average by a factor of 1.77, if either star is equally likely to host the planet. Lastly, we find the planetary radius gap is robust to the impact of dilution.