Effects of dimensionality on magnetic and electric properties of one- and two-dimensional GeMn systems and the role of defects in magnetic ordering are investigated by means of electron spin resonance (ESR) and superconducting quantum interference device magnetometry techniques. Arrays of Ge1-xMnx nanowires and thin Ge:Mn films with similar concentrations of the magnetic impurity (x=1%-8%) have been fabricated by chemical synthesis and ion implantation, respectively. In magnetically homogeneous Ge1-xMnx nanowires, all observed electron spin resonances are related to absorption on individual magnetic centers (Mn3+ and Mn2+ ions and polarized charge carriers) in a broad temperature range, T=5-300 K. On the other hand, in strongly inhomogeneous 2D GeMn films, a collective spin excitation, the spin-wave resonance, is observed at low temperatures, T=5-60 K. This signifies the presence of long-range spin states and a cooperative magnetic response originating from crystalline Mn5Ge3 precipitates and Mn-rich amorphous nanoclusters as well as diluted Mn ions. Additionally, a strong negative background was observed and attributed to the microwave magnetoresistance of the Ge:Mn thin films. The absence of the magnetoresistance in Ge1-xMnx nanowires indicates that the scattering of charge carriers is determined by dimensions of the structure. Overall, our analysis of magnetic-resonance phenomena reveals a significant difference between one-dimensional and two-dimensional magnetic semiconductors. It emphasizes the important role of dimensionality as well as the type and distribution of magnetic defects in spin-dependent scattering and dynamic magnetic properties of GeMn semiconductors.