We present measurements of the CP-violation parameters S and C for the radiative decay B^0 → ηK^0_Sγ for B → ηKγ we also measure the branching fractions and for B^+ → ηK^+γ the time-integrated charge asymmetry A_(ch). The data, collected with the BABAR detector at the Stanford Linear Accelerator Center, represent 465 × 10^6 BB pairs produced in e^+e^- annihilation. The results are S = -0.18^(+0.49)_(-0.46) ± 0.12, C = -0.32^(+0.40)_(-0.39) ± 0.07, B(B^0 → ηK^0γ) = (7.1^(+2.1)_(-2.0) ± 0.4) × 10^(-6), B(B^+ → ηK^+γ) = (7.7 ± 1.0 ± 0.4) × 10^(-6), and A_(ch) = (-9.0^(+10.4)_(-9.8) ± 1.4) × 10^(-2). The first error quoted is statistical and the second systematic