Yes, large bags are permitted into the theatre, but if they're too large to fit in the under seat compartment, just leave it on the floor in front of you and a CM will move it to the side. Yes, it will be right there when you return. No, no one will touch your stuff. Also, no guest is allowed to stand on the floor while the ride is in the air. The only person on ground floor is the CM in the Tower position watching the video monitors. All the other Cast scan their rows and the areas, then safely leave the theatre before the flight is initiated. It's also the Tower CM's duty to check the cameras looking at the ground floor to check for "lost" guests.