The interplay between current and magnetization fluctuations and dissipation in layered-ferromagnetic-normal-metal nanostructures is investigated. We use scattering theory and magnetoelectronic circuit theory to calculate charge and spin-current fluctuations. Via the spin-transfer torque, spin-current noise causes a significant enhancement of magnetization fluctuations. A special focus is on spin valves in which one of the ferromagnets is pinned. We find that the magnetization noise and damping are tensors that depend on the magnetic configuration. For symmetric spin valves in which both layers fluctuate, dynamic cross-talk between the layers becomes important, causing a possibly large difference in noise level between the parallel and antiparallel magnetic configurations. Due to giant magnetoresistance (GMR), the magnetization fluctuations in spin valves induce resistance noise, which is identified as a prominent source of electric noise at relatively high current densities. The resistance noise is shown to vary considerably with the magnetic configuration, partly due to the dependence of the angular GMR. The contribution from spin-current fluctuations to the resistance noise is shown to be significant. Resistance noise is an experimentally accessible quantity that can be measured to verify our results.