My understanding of the fat fast, which I've done a few times and am currently doing today and tomorrow, is that it is OK to do cardio and stretching routines. Weightlifting should be avoided, though, because you aren't consuming enough protein to repair the muscle damage caused by lifting, which is what causes muscle growth. If you can't repair the damaged muscle, you end up losing muscle instead.

I usually don't have a problem with energy while fat fasting. I follow it strictly: 6 ounces cream cheese, 2 ounces macadamias spread throughout the day and I can do my usual cardio workout with no problem.