Fasting all day then eating sounds like a poor plan to me as it revs up your metabolism at the wrong time of day. I would say either fast, or eat a sensible diet 3 meals a day plus healthy snacks for weight loss. The key to weight loss, of coure, is to burn more calories than you are taking in.
The fasting/eating plan you talk about sounds like a recipe for disaster -- your body will become confused and start storing extra calories instead of burning them!
No reason you couldn't start a moderate exercise program while fasting if you are feeling strong. The thing is not to overdo it, and take a day off if you need to.