These should be only washed with like colors. You can certainly machine wash the garments in warm water that is around 104°F/40°C. Keep in mind that you should only use non-chlorine bleach if necessary and do not iron the decorated (printed) areas. If the garments require dry-cleaning, you can use any solvent except the trichloroethylene. Tumble-dry these garments on medium.
The pillowcase itself can be machine washed according to the above mentioned care instructions. However, the pillow instert should only be handwashed.