To move a sleeping cat, I find that slipping both hands underneath and spreading them to keep the cat in as close to the same position as possible usually works....
Yes, you may draw pictures, as long as you can understand what you drew. Keeping consistent with the organizer makes for easy reviewing, but pictures and words may be added.
Yes, if they aren't overwritten. If it happened on your phone or anything else not running Windows, than turn off your device immediately, since Android and Apple's iPhones, iPads, etc....