We haven't tested mylar yet, but are adding to our list! We have cut it on our Cricut but it did require quite a few passes. We aren't sure that it would work in the Aura machine since it's a translucent material. It looks like others have used it in the Glowforge Plus and Pro, though.
You can definitely do that! You might run into the little pieces falling through the crumb tray but you can just remove the tray and retrieve your cuts.