We consider modulation space and spaces of Schatten-von Neumann symbols where corresponding pseudo-differential operators map one Hilbert space to another. We prove Hölder-Young and Young type results for such spaces under dilated convolutions and multiplications. We also prove continuity propertiesfor such spaces under the twisted convolution, and the Weyl product. These results lead to continuity properties for twisted convolutions on certain weighted Lebesgue spaces with Lebesgue parameter at most 2.