Observation of B+->(K)over-bar(0) K+ and B-0 -> K-0 (K)over-bar(0)

We report observations of the b -> d penguin-dominated decays B+->(K) over bar K-0(+) and B-0 -> K-0(K) over bar (0) in 316 fb(-1) of e(+)e(-) collision data collected with the BABAR detector. We measure the branching fractions B(B+->(K) over bar K-0(+))=(1.61 +/- 0.44 +/- 0.09)x10(-6) and B(B-0 -> K-0(K) over bar (0))=(1.08 +/- 0.28 +/- 0.11)x10(-6) and the CP-violating charge asymmetry A(CP)((K) over bar K-0(+))=0.10 +/- 0.26 +/- 0.03. Using a vertexing technique previously employed in several analyses of all-neutral final states containing kaons, we report the first measurement of time-dependent CP-violating asymmetries in B-0 ->(KSKS0)-K-0, obtaining S=-1.28(-0.73-0.16)(+0.80+0.11) and C=-0.40 +/- 0.41 +/- 0.06. We also report improved measurements of the branching fraction B(B+-> K-0 pi(+))=(23.9 +/- 1.1 +/- 1.0)x10(-6) and CP-violating charge asymmetry A(CP)(K-0 pi(+))=-0.029 +/- 0.039 +/- 0.010.