Reference the Hotkeys: This is an option in the Show Menu. When you begin a Show (ie. select the students to be included within the show), there is also a checkbox on that option screen which enables the Show Hotkeys feature.
Ref the wallpaper issue, I believe this is by design - if this is unchecked, the wallpaper will be missing until the session is complete. as long as the Tutor / Instructor is connected to the Student machine and the current user stays logged in, the wallpaper will remain disabled.
Hope this helps.