[en] We report new high-precision measurements of p(r vec γ,γ), p(r vec γ,π⁰) and p(r vec γ,π⁺) cross section and beam asymmetry angular distributions for photon beam energies in the range from 213 MeV to 333 MeV. The cross sections for all three channels are locked together with a small common systematic scale uncertainty of 2%. A large overdetermination of kinematic parameters was used to achieve the first complete separation of the Compton scattering and π⁰-production channels. This has also allowed all detector efficiencies for the p(rvec γ,γ) and p(rvec γ,π⁰) channels to be measured directly from the data itself without resorting to simulations. The new Compton results are approximately 30% higher than previous Bonn data near the peak of the Δ resonance, resolving a long-standing unitarity puzzle. However, our p(rvec γ,π⁰) and p(rvec γ,π⁺) cross sections are also about 10% higher than both earlier Bonn data and recent Mainz measurements, while our p(rvec γ,π⁺) cross sections are in good agreement with results from Tokyo. Our polarization asymmetry data are of the highest precision yet available and have considerable impact upon multipole analyses. These new data have been combined with other polarization ratios in a simultaneous analysis of both Compton scattering and π production, with Compton scattering providing two new constraints on the photopion amplitude. This analysis has improved the accuracy in the E2/M1 mixing ratio for the N→Δ transition, EMR=-[3.07±0.26(stat+syst)±0.24(model)](%), and the corresponding N→Δ transverse helicity amplitudes, A_1/2=-[135.7±1.3(stat+syst)±3.7(model)](10^-3GeV^-1/2) and A_3/2=-[266.9±1.6(stat+syst)±7.8(model)](10^-3GeV^-1/2). From these we deduce an oblate spectroscopic deformation for the Δ⁺. The same simultaneous analysis has been used to extract the proton dipole polarizabilities, bar α-bar β=+[10.39±1.77(stat+syst)_-1.87^+1.02(model)](10^-4fm³) in agreement with previous low energy measurements, and bar α+bar β=+[13.25±0.86(stat+syst)_-0.58^+0.23(model)](10^-4fm³) in agreement with recent evaluations of the Baldin sum rule. Our simultaneous analysis has also provided the first determination of the proton spin polarizabilities, γ_π=-[27.23±2.27(stat+syst)_-2.10^+2.24(model)](10^-4fm⁴), γ₀=-[1.55±0.15(stat+syst)_-0.03^+0.03(model)](10^-4fm⁴), γ₁₃=+[3.94±0.53(stat+syst)_-0.18^+0.20(model)](10^-4fm⁴),and γ₁₄=-[2.20±0.27(stat+syst)_-0.09^+0.05(model)](10^-4fm⁴).The extracted value of the backward spin polarizability, γ_π, is considerably different from other analyses and this has been instrumental in bringing the value of bar α-bar β extracted from high energy data into agreement with low energy experiments.