We present measurements of the branching fractions for the decays B -> K mu(+)mu(-) and B -> Ke(+)e(-), and their ratio (R-K), using a data sample of 711 fb(-1) that contains 772 x 10(6) B (B) over bar events. The data were collected at the Gamma(4S) resonance with the Belle detector at the KEKB asymmetric-energy e(+)e(-) collider. The ratio RK is measured in five bins of dilepton invariant-mass-squared (q(2)): q(2) is an element of (0.1, 4.0), (4.00, 8.12), (1.0, 6.0), (10.2, 12.8) and (> 14.18) GeV2/c(4), along with the whole q(2) region. The R-K value for q(2) is an element of (1.0, 6.0) GeV2/c(4) is 1.03(-0.24)(+0.28) +/- 0.01. The first and second uncertainties listed are statistical and systematic, respectively. All results for R-K are consistent with Standard Model predictions. We also measure CP-averaged isospin asymmetries in the same q(2) bins. The results are consistent with a null asymmetry, with the largest difference of 2.6 standard deviations occurring for the q(2) is an element of (1.0, 6.0) GeV2/c(4) bin in the mode with muon final states. The measured differential branching fractions, dB/dq(2), are consistent with theoretical predictions for charged B decays, while the corresponding values are below the expectations for neutral B decays. We have also searched for lepton-flavor-violating B -> K mu(+/-)e(-/+) decays and set 90% confidence-level upper limits on the branching fraction in the range of 10(-8) for B+ -> K+ mu(+/-)e(-/+), and B-0 -> K-0 mu(+/-) e(-/+) modes.