We report on the structural and magnetic properties of thin Ge1-xMnx films grown by molecular beam epitaxy (MBE) on Ge(001) substrates at temperatures (T-g) ranging from 80 to 200 degrees C, with average Mn content between 1% and 11%. Their crystalline structure, morphology, and composition have been investigated by transmission electron microscopy (TEM), electron energy loss spectroscopy, and x-ray diffraction. In the whole range of growth temperatures and Mn concentrations, we observed the formation of manganese-rich nanostructures embedded in a nearly pure germanium matrix. The growth temperature mostly determines the structural properties of Mn-rich nanostructures. For low growth temperatures (below 120 degrees C), we evidenced a two-dimensional spinodal decomposition resulting in the formation of vertical one-dimensional nanostructures (nanocolumns). Moreover, we show in this paper the influence of growth parameters (T-g and Mn content) on this decomposition, i.e., on the nanocolumn size and density. For temperatures higher than 180 degrees C, we observed the formation of Ge3Mn5 clusters. For intermediate growth temperatures, nanocolumns and nanoclusters coexist. Combining high-resolution TEM and superconducting quantum interference device magnetometry, we could evidence at least four different magnetic phases in Ge1-xMnx films: (i) paramagnetic diluted Mn atoms in the germanium matrix, (ii) superparamagnetic and ferromagnetic low-T-C nanocolumns (120 <= T-C <= 170 K), (iii) high-T-C nanocolumns (T-C >= 400 K), and (iv) Ge3Mn5 clusters.