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Short answer: For a close-to-optimal representation, instead of Coulomb-wave functions, use spherical harmonics for the angular part and a grid-like representation in radial direction. ("grid-like" means finite-differences, collocation methods, discrete-variable-representations, or similar methods).
Long answer: The usual approach to solving the Hartree-...
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Most of your answers look good. For the geometry optimization of single-reference organic systems, B3LYP/big should be fine. MPn is bad for open-shell systems in general. MCSCF is the way to go if one has truly pathological multireference effects. CCSD(T)/huge is good any time you want to treat dispersion, but you'll find in the literature that (He)2 ...
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