i have seen them on those rentable climbing walls at events and fairs. you just hook the rope up to your harness and climb. if the person falls it lets them down slowly.
Yes. Those devices are commonly used in action movies and rock climbing.
I bungee cord, make sure you tie it up good =D
They're called autobelay or auto-belay devices. (Very creative naming, that.) You can find them in many climbing gyms. When not in use, the end of the cable (not a rope) is normally clipped to the wall at the bottom of the route. In climbing gyms it's kind of a nuisance if the last person to use it lets the carabiner retract 60 feet up in the air ;-)
Autobelayers, Red Point (an autobelay company) just recalled thousands of them due to a brake failure because of bad bearings. Heres the recall link: www.recalls .au/content/index....
