Can I put the cover in the washing machine?
With Peg-Pérego strollers, you can officially machine wash the covers, yes. On the other hand, the fabrics tend to fade quite a lot over thíme, and the washing in the machine makes it worse. I recommend hand washing it only, here's an article why it's better and how to clean and maintain your stroller to keep it in a good shape.
So, you theoretically can machine wash it, but it's not optimal and you might damage the textiles. Do consider spot and hand cleaning if the dirt is not extreme.