Answer: No and no. Some religions call for occasional fasts, and some people derive satisfaction from fasting. But a fast won't "cleanse" your body of "toxins" in any way. There's no evidence that your body needs internal cleansing or that the digestive system needs a "rest."
Your digestive system is quite efficient at cleansing itself and ridding the body of waste. That's one of its chief purposes, and other organs (the kidneys, liver, lungs, sweat glands) help, too. The notion that stagnation and decay in the colon produce toxins that poison the body is an ancient one, but long ago discredited.
Still, countless websites, books, and alternative practitioners promote fasts, lasting anywhere from a few days to two weeks, to detoxify the body. The mysterious toxins, never named, are supposed to cause everything from headaches, colds, and skin problems to heart disease and mental disorders.
Not surprisingly, total fasting does result in a rapid initial weight loss, but most of the loss is fluid, rather than fat. As the fast continues, you lose body fat, but also considerable muscle (including heart muscle) and minerals. Depending on the duration of the fast, the muscle and mineral loss can be dangerous. In any case, few people who actually lose weight via fasting maintain their loss once they start eating again.
For a person in good health, there is no danger in a 24-hour fast. Beyond a day or two, fasting can cause fatigue, headaches, irritability, nausea, low blood pressure, and heart rhythm problems. It is especially hazardous for anyone with a chronic illness such as diabetes or liver or kidney disease. When fasting, it's important to drink plenty of water. And, of course, pregnant women shouldn't fast.