Train your body to burn fat while exercising in a healthy way
Keep in mind that other things like stress, sleep, nutrition can all affect your heart rate on different days and at different times of day so this is more of like a 'range' thing that a 'for sure thing' in a practical setting. Trying to exercise at the same time of day every day may be ideal.
1) Do strength training (build some muscles)
Even at resting (doing nothing) muscle cells burns more energy (calories) than fat cells. So the more muscles you have, the more energy (calories) you'll be burning even while sitting and watching TV.
2) Don't make it a habit to exercise for a prolonged period after fasting:
Yes, in the short term you'll burn more fat. But your body will respond to it in an unhealthy way. Remember how muscles require more calories even if you are doing nothing when compared with fat cells? Well your body is built for survival, so if you constantly exercise in this way, your body will actually respond by getting rid of muscle cells and storing more fat cells to prepare for those times when you expend energy on an empty stomach.
Plus, there will be more stress hormones in your system which just isn't very good for you overall. Do yourself a favor and don't try this unless you are a body builder who needs that extra loss of fat right before an competition.
3) Low to mid intensity for long time or high intensity? All of them.
Without getting into the details too much, it doesn't really matter how you end up burning 300 calories when you exercise. Eventually, some of it has to come from your fat storage. Personally, I like high intensity aerobic exercises because they are more time efficient, activate more muscle fibers and generally translates well in terms of performance in sports. However, if you do only high intensity workouts, you're at a higher risk for injury and more prone to "burning-out" which impedes you from reaching your goal (of losing fat) in the long run. Low to mid intensity aerobic activity can be good for days when you need to take it easy to allow your body to heal. In general, it is good to vary your workouts to keep yourself motivated and avoid overuse injury.
4) Eat right (Balanced Diet)
Honestly, if you don't eat a balanced diet, it matters very little what you do in terms of exercise. If you are putting in work in the gym and you're still not seeing the results you want (lose body fat), it may be a good idea to track your nutrition intake.