We present a measurement of the branching fractions and charge- parity-( CP-) violating parameters in B..K decays. The results are obtained from the final data sample containing 772 x 10(6) BB _ pairs collected at the.d4S_ resonance with the Belle detector at the KEKB asymmetric- energy e_e- collider. We obtain the branching fractions BdB0 0 d4.5 0.4dstat 0.3dsyst_x10- 6; BdB_..K__ d6.80.4dstat_ 0.4dsyst__x10- 6 which are in agreement with their respective current world averages. For the CP- violating parameters, we obtain A.K0 S - 0.36 +/- 0.19dstat_ 0.05dsyst_; S.K0 S 0.91 0.32dstat 0.05dsyst_; A.K_ - 0.03 +/- 0.04dstat_ 0.01dsyst_; where A and S represent the direct and mixing- induced CP asymmetry, respectively. We find no evidence of CP violation in the decay channel B_..K_; however, we obtain the first evidence of CP violation in the B0..K0 S decay channel at the level of 3.1 standard deviations.