  We present preliminary measurements of branching fractions and CP-violating
asymmetries in decays of B mesons to two-body final states containing a K0. The
results are based on a data sample of approximately 227 million Upsilon(4S)
decays collected with the BABAR detector at the PEP-II asymmetric-energy B
Factory at SLAC. We measure BF(B+ --> K0pi+) = (26.0 +/- 1.3 +/- 1.0) x 10-6,
BF(B+ --> K0barK+) = (1.45 +0.53 -0.46 +/- 0.11) x 10-6 (< 2.35 x 10-6), and
BF(B0 --> K0K0bar) = (1.19 +0.40 -0.35 +/- 0.13) x 10^-6, where the first
uncertainty is statistical and the second is systematic, and the upper limit is
at a 90% confidence level. The significance of the BF(B+ --> K0barK+) and BF(B0
--> K0K0bar) results are 3.5 sigma and 4.5 sigma, respectively, including
systematic uncertainties. In addition, we obtain a measurement of the
CP-violating asymmetry for the BF(B+ --> K0pi+) mode and we determine a 90%
confidence-level interval for the asymmetry in the BF(B+ --> K0barK+) mode:
ACP(B+ --> K0pi+) = -0.087 +/- 0.046 +/- 0.010 and ACP(B+ --> K0barK+) is in
[-0.43, 0.68].
