The effects of the geometric phase and non-adiabatic coupling induced by the conical intersection between the two lowest electronic potential energy surfaces are investigated for the H + H(2) collision and H(3) predissociation. The strongest effect of the geometric phase at all collision energies is a significant change in the ortho -> ortho and para -> para differential cross-sections, which is due to a sign change in the interference between reactive and non reactive contributions. This is caused by the indistinguishability of the three interacting atoms. At high energies (3.5 eV above collision threshold and more), a significant dynamical effect appears in the differential cross-sections. This effect is related to a sign change in the interference between two dynamical paths (direct and looping contributions) connecting reagents to products. Both these symmetry and dynamical effects almost completely disappear in the integral cross-sections. Electronic non-adiabatic couplings are efficient in turning the bound states supported by the cone of the first excited electronic adiabatic potential into resonances which have significant effects only on transitions between excited reagents and products. The study of the decay of these resonances provides clues for the understanding of the experimental results in the predissociation of Rydberg states of H(3).