Yes! Make sure you have several points to attach and maybe a piece of wood attached to the panel, instead of adding screws directly into the panels. The material might still be fragile, and therefore normal screws might damage the material. Be careful and use screws with a large cap into the material.
No, this is not possible. Sanding the panels will result in the loss of the mycelium skin surrounding the panel.
Yes, to a certain extent. You can cut the panels. Take into account that the cut parts will be fibrous, as this is the inside of the mycelium composite. To avoid any loss of fibres or strength, you could add a bio-based coating.