Spin-polarization and magnetic damping are measured for several polycrystalline films with each of them being made of a different single Co2Mn-based Heusler compound. As several epitaxial Co2Mn-based Heusler compounds are shown to be half-metal magnetic materials with full spin-polarization and ultralow magnetic damping, we explore here these properties but in polycrystalline films. Co2MnSi, Co2MnGe, and Co2MnGa thin films were grown on glass substrates and analyzed in situ by electron diffraction and spin-resolved photoemission and ex situ by transmission electron microscopy and ferromagnetic resonance. Despite the polycrystalline state of the films, they still exhibit high spin polarizations and very low magnetic damping coefficients. The latter are at least of the same order as the best epitaxial films using regular ferromagnetic materials. The key point to achieve such properties is to control the Heusler stoichiometry as best as possible.