Relative fractions B0(d),s --> h+ h'- decays (where h, h' = K or
pi) and the direct CP asymmetry A_CP in the B0(d) --> K+ pi- mode are
measured with 179 +/- 11 pb-1 of data collected using the CDF II detector
at the Fermilab Tevatron p anti-p collider.  The first branching-fraction
measurement of a B0(s) meson to two pseudoscalars, B(B0(s) --> K+ K-), and
a search for the baryon mode Lambda0_ b --> p+ h- are also presented, in
addition to branching-fraction limits on the rare channels B0(s) --> K+
pi-, B0(d) --> K+ K-, and B0(s) --> pi+ pi-.