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, collected 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 forward-backward asymmetry of the light meson in the p¯p rest frame is measured. No significant CP asymmetry in B+→p¯pK+ decay is found in any region of the Dalitz plane. We present the first observation of the decay B+→¯¯¯Λ(1520)(→K+¯p)p near the K+¯p threshold and measure B(B+→¯¯¯Λ(1520)p)=(3.9+1.0−0.9(stat)±0.1(syst)±0.3(BF))×10−7, where BF denotes the uncertainty on secondary branching fractions.