If you are doing a water fast, then it is water and nothing but water. No coffee, supplements, teas or anything else. No exercise should be done on a Water Fast except gentle stretching and occasional slow walking. A true Water Fast is not for losing weight, it is for cleansing and healing. Some describe it as knife-less surgery. Any compromise will lessen the benefits of the fast. Don't worry about weight loss while water fasting, in fact, stay off the scales. I admit I approach Water Fasting from a medicinal healing point of view. Those who embrace fasting as a method of rapid weight loss have a fasting for weight loss forum where pretty much anything goes.
One more thing-take time to wean yourself off coffee before beginning your fast, otherwise you will probably suffer the worst caffeine withdrawal migraines of your life.