High-precision quantum-mechanical calculations have been developed to investigate positronium (Ps) scattering. Positronium scattering experiments are a powerful tool to study positronium-matter interactions, but the theoretical description of these experiments needs better accuracy. We have developed an ab initio confined variational approach that can reach higher collision energy, includes higher orbital momenta and uses small confining radii. Calculation of the Ps-He momentum-transfer cross section shows that the experimental Doppler broadening spectroscopy results are questionable. The energy dependence of the pickoff annihilation rate is also calculated, demonstrating an important role of the so far neglected P-wave contribution.