No, it is not possible to fast for that long and expect to be alive for all of it especially with out water. Any real person cannot survive without food for 3 weeks, so instead what is used is a suspension of belief. What a suspension of belief is when a writer introduces something that can be a little believable and makes it interesting, then it would make the readers forget about reality and just focus on the story. In the version of Cinderella that I read which was “The Little Red Fish And the Golden Clog”. There where many occasions that wasn’t believable at all like a fish that can talk and toxics that can make a person beautiful, but what made it ok was the emotions of Cinderella and how she was being treated a version of suspension of belief. A another example, is a super hero show called the Flash the main character was hit by lighting next to random chemicals. In real life a person would die by the chemicals and the lighting, but it would be entertaining to see a human get super speed and it kind of makes sense. As the watcher you do not know what chemicals that are used and with the way how science is now it is possible. The fact that the chemicals could of fuse with the lighting and in return it gave him powers could be excused.