We present measurements, based on a sample of approximately 23x10(6) BB pairs, of the branching fractions and a search for CP-violating charge asymmetries in charmless hadronic decays of B mesons into two-body final states of kaons and pions. We find the branching fractions B(B0-->pi(+)pi(-)) = (4.1+/-1.0+/-0.7)x10(-6), B(B0-->K+pi(-)) = (16.7+/-1.6+/-1.3)x10(-6), B(B+-->K+pi(0)) = (10.8(+2.1)(-1.9)+/-1.0)x10(-6), B(B+-->K0pi(+)) = (18.2(+3.3)(-3.0)+/-2.0)x10(-6), B(B0-->K0pi(0)) = (8.2(+3.1)(-2.7)+/-1.2)x10(-6). We also report 90% confidence level upper limits for B meson decays to the pi(+)pi(0), K+K-, and K0K+ final states. In addition, charge asymmetries have been found to be consistent with zero, where the statistical precision is in the range of +/-0.10 to +/-0.18, depending on the decay mode.