Hi Mariaan

There's no truth that you must keep heart rate down to burn fat. You burn fat no matter what your heart rate is, the trick is to find the right balance between exercising hard enough to burn more fat, and exercise easy enough so that you can actually do exercise for a long period. If you go out and run as hard as you can, you will actually burn fat at a greater rate than if you go out and run slowly. However, the problem is that you can only run flat out for about a minute or two, whereas you can probably do an hour or so if you go slowly enough. So there is a balance between going hard and going easy, and the trick is to find it. People often use heart rate as a guide, and it can work, but I personally don't think that heart rate is that accurate - the problem is that your 70% may well be quite different to another's, because everyone is different and so making these general guidelines just doesn't work.
I like the example of Janine on the forum - she is right, you have to go for long enough, but also hard enough, and so my advice is that you find an exercise intensity that allows you to exercise for say 45 minutes feeling tired, but not exhausted. You should always feel that by about 2 hours after finishing, you still have something left in the tank, so to speak. if you don't, then you are training too hard. if you feel good right away, then you can probably exercise a little harder.

As for not eating, that won't really work either, all it will do is compromise your trainign session because you will run out of energy. Try not to complicate things - just go out, don't worry about when you ate (except for eating too close to when you exercise, of course, because then you have stomach troubles) and just exercise and make sure you eat well, and things will happen.

Good luck