The extremely accurate estimates of stellar variability and radial velocity in the Gaia Data Release 3 (Gaia DR3) have enabled us to examine the close binarity and radial velocity (RV) of central stars (CSs) of planetary nebulae (PNe). This study is twofold: (1) searching for new close binary CS candidates to better understand how binarity affects the formation and evolution of PNe; and (2) extending the sample size of known RVs of PNe in order to understand their kinematics and the dynamics of the Milky Way. As a target sample, we used all true, possible, and likely PNe available in the literature. Then, we looked for their matched Gaia DR3 sources that provide measurements of variability and RV. As a result, we detected the first large collection of trustworthy photometric variability of 26 symbiotic stars and 82 CSs. In this CS group, there are 24 sources already classified as true close binary CSs in the literature. Hence, we discovered 58 new close binary CS candidates. This close binary (CB) sample represents more than half of what is currently available in the literature. In addition, we identified the radial velocities for 51 PNe. To our knowledge, 24 of these were measured for the first time. The RV measurements predicted by Gaia, based on the Doppler shift of the CS absorption lines, and those derived from nebular emission lines, show satisfactory agreement except for a few extremely high-velocity PNe.