When I decided to lose a lot of weight 12 years ago, cutting out all liquid calories and cutting WAY down on all starchy carbs (bread, potatoes, pasta, rice, etc.) worked wonders. Also a lot of exercise. Granted, I've come to believe that weight loss is 70% diet and 30% exercise, but when I'm exercising regularly I notice I didn't have the cravings to snack at night that I used to. I am also more motivated to stick with the proper diet. There's a real synergistic effect between diet and exercise.
Always better to exercise in a fasted state, the body produces Ketones when it runs out of Glycogen, and the brain actually functions better on Ketones, which is why people actually feel sharper mentally when in a fasted state.