Heterostructures of Co-doped ZnO and Permalloy were investigated for their static and dynamic magnetic interaction. The highly Co-doped ZnO is paramagentic at room temperature and becomes an uncompensated antiferromagnet at low temperatures, showing a narrowly opened hysteresis and a vertical exchange bias shift even in the absence of any ferromagnetic layer. At low temperatures in combination with Permalloy an exchange bias is found causing a horizontal as well as vertical shift of the hysteresis of the heterostructure together with an increase in coercive field. Furthermore, an increase in the Gilbert damping parameter at room temperature was found by multifrequency FMR evidencing spin pumping. Temperature dependent FMR shows a maximum in magnetic damping close to the magnetic phase transition. These measurements also evidence the exchange bias interaction of Permalloy and long-range ordered Co-O-Co structures in ZnO, that are barely detectable by SQUID due to the shorter probing times in FMR.