Is the mug dishwasher/microwave safe? Are there washing instructions for the clothing?

Yes to both, with real caveats depending on the product/technique:

• La Vieya mug: dishwasher and microwave safe according to Printful, though they recommend hand-washing to keep it in better shape over time.
• T-shirts and hoodies (DTG and DTFlex): machine wash, cold water, inside out, gentle cycle, no fabric softener; line dry or tumble dry on low heat; iron cold, inside out, never directly on the print.
• Embroidered cap: hand wash only — machine washing can warp it and damage the embroidery.