We present updated measurements of the branching fractions for B 0 meson decays to η K 0 , η η , η ϕ , η ω , η ′ K 0 , η ′ η ′ , η ′ ϕ , and η ′ ω , and branching fractions and C P -violating charge asymmetries for B + decays to η π + , η K + , η ′ π + , and η ′ K + . The data represent the full data set of 467 × 10 6 B ¯¯¯ B 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 B 0 → η ′ K 0 , we find evidence for three B 0 decay modes at greater than 3.0 σ significance. We find B ( B 0 → η K 0 ) = ( 1.15 + 0.43 − 0.38 ± 0.09 ) × 10 − 6 , B ( B 0 → η ω ) = ( 0.94 + 0.35 − 0.30 ± 0.09 ) × 10 − 6 , and B ( B 0 → η ′ ω ) = ( 1.01 + 0.46 − 0.38 ± 0.09 ) × 10 − 6 , where the first (second) uncertainty is statistical (systematic). For the B + → η K + decay mode, we measure the charge asymmetry A ch ( B + → η K + ) = − 0.36 ± 0.11 ± 0.03 .