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Abstract We investigate the fundamental three-body Coulomb process of elastic electron-positronium (e^--Ps) scattering below the Ps(n = 2) threshold. Using the complex Kohn variational method and trial wave functions that contain highly correlated Hylleraas-type terms, we accurately compute^1,3S-,^1,3P-, and^1,3D-wave phase shifts, which may be considered as benchmark results. We explicitly investigate the effect of the mixed symmetry term in the short-range part of the^1,3D-wave trial wave function on the phase shifts and resonances. Using the complex Kohn phase shifts we compute, for e⁻-Ps scattering, the elastic differential, elastic integrated, momentum-transfer, and ortho-para conversion cross sections and determine the importance of the complex Kohn D-wave phase shifts on these cross sections. In addition, using the short-range part of the¹S-wave trial wave function for the bound state of the purely leptonic ion of Ps⁻, and the complex Kohn¹P trial wave function for the continuum state, we determine the Ps⁻photodetachment cross section in the length, velocity, and acceleration forms.