The cosmic microwave background (CMB) anisotropies are difficult to measure at large angular scales. In this paper, we present a new analysis of the Planck High Frequency Instrument data that brings the cosmological part and its major foreground signal close to the detector noise. The solar dipole signal induced by the motion of the Solar System with respect to the CMB is a very efficient tool for calibrating a detector or cross-calibrating sets of detectors with high accuracy. In this work, the solar dipole signal is used to extract corrections of the frequency map offsets, reducing uncertainties significantly. The solar dipole parameters are refined together with the improvement of the high-frequency foregrounds and the CMB large-scale cosmological anisotropies. The stability of the solar dipole parameters is a powerful way to control Galactic foreground removal in the component separation process. We use this stability to build a model of the spatial variations in spectral energy distribution of the interstellar dust emission. Knowledge of these variations will help future CMB analyses of intensity and polarization used to measure faint signals related to the optical reionization depth and the tensor-to-scalar ratio of the primordial anisotropies. The results of this work are: improved solar dipole parameters, a new interstellar dust model, and a large-scale intensity map of cosmological anisotropies.