We describe studies of the decays of B mesons to final states {eta}K{sup *}(892), {eta}K{sup *}{sub 0}(S-wave), {eta}K{sup *}{sub 2}(1430), and {eta}'K based on data collected with the BABAR detector at the PEP-II asymmetric-energy e{sup +}e{sup -} collier at the Stanford Linear Accelerator Center. We measure branching fractions and charge asymmetries for the decays B {yields} {eta}K{sup *}, where K{sup *} indicates a spin 0, 1, or 2 K{pi} system, making first observations of decays to final states {eta}K{sup *0}{sub 0}(S-wave), {eta}K{sup *+}{sub 0} (S-wave), and {eta}K{sup *0}{sub 2}(1430). We measure the time-dependent CP-violation parameters S and C for the decays B{sup 0} {yields} {eta}'K{sup 0}, observing CP violation in a charmless B decay with 5{sigma} significance considering both statistical and systematic uncertainties..