Dynamics and direct CP violation in three-body charmless decays of charged B mesons to a proton, an antiproton and a light meson (pion or kaon) are studied using data, corresponding to an integrated luminosity of 1:0 fb(-1), llected by the LHCb experiment in pp collisions at a center-of-mass energy of 7 TeV. Production spectra are determined as a function of Dalitz-plot and helicity variables. The forwardbackward asymmetry of the light meson in the p (p) over bar rest frame is measured. No significant CP asymmetry in B+ -> p (p) over barK(+) decay is found in any region of the Dalitz plane. We present the first observation of the decay B+ -> (Lambda) over bar (1520)(-> K+(p) over bar )p near the K+(p) over bar threshold and measure B(B+ -> (Lambda) over bar (1520)p) = (3.9(-0.9)(+1.0)(stat) +/- 0.1 (syst) +/- 0.3 (BF)) x 10(-7), where BF denotes the uncertainty on secondary branching fractions.