We present updated measurements of the branching fractions for B0 meson decays to etaK0, etaeta, etaphi, etaomega, eta'K0, eta'eta', eta'phi, and eta'omega, and branching fractions and CP-violating charge asymmetries for B+ decays to etapi+, etaK+, eta'pi+ and eta'K+. The data represent the full dataset of 467 10^{6} BB pairs collected with the BaBar detector at the PEP-II asymmetric-energy e+e- collider at the SLAC National Accelerator Laboratory. Besides large signals for the four charged B decay modes and for B0\to eta'K0, we find evidence for three B0 decay modes at greater than 3.0sigma significance. We find B(B0\to etaK0) = (1.15^{+0.43}_{-0.38} \pm0.09)x10^{-6}, B(B0\to etaomega) = (0.94^{+0.35}_{-0.30}\pm0.09)x10^{-6}, and B(B0\to eta'omega) = (1.01^{+0.46}_{-0.38}\pm0.09)x10^{-6}, where the first (second) uncertainty is statistical (systematic). For the B+\to etaK+ decay mode, we measure the charge asymmetry A_{ch}(B+\to etaK+) = -0.36 \pm 0.11 \pm 0.03. Show Partial Abstract