I've completed a 7, 8, and a 14 day water fast; well, I did continue to drink coffee with no caloric sweeteners.
It is incredibly therapeutic - after the 14 day fast I had brought my diastolic blood pressure down about 12 points. It remains 10 points down, after more than a year. I feel much better, my energy is better and I'll guarantee you I don't look nearly as bad as most 58 year olds.
There actually is research, it can help repair DNA, induce autophagy and help with cellular housekeeping mechanisms. As mentioned, muscle sparing hormones are dramatically increased during fasting, and you are burning fat. Most people without cardiac or kidney problems should be able to do about 45 days with no physical harm. They say that your body knows when you have reached your absolute limit, and you will be ravenously hungry.
An extremely important thing is properly breaking a long fast, you can't just go eating tons of food immediately; the rush of glucose could send you into shock and kill you, gotta take it slow. Supposedly the mucous lining in the stomach is also thinner, and takes a couple days of light eating (like watermelon and cantalope) to come back fully. The second fast, I broke it wrong and regretted it.
However, each and every time, I experienced long term relief from my gastric reflux. After the 14 day fast, I've only had a few issues and that's when I eat and drink way too much or close to bedtime. It is an amazing experience.