HIIT for 1 hour would not be HIIT.. it's high intensity interval training. If you can do HIIT for 1 hour, you're probably not doing HIIT but just regular interval training.
As far as the fat burning zone.. the fat burning zone, if I remember correctly, has been established at somewhere around 66% of max heart rate, with HIIT you will be much higher. However, the fat burning zone is just where the highest % of the calories you burn will come from fat, a number in % does not take into account the total number of calories burned. Let's say you do steady state cardio in the fat burning zone and you burn 500 calories, 250 of them being from fat, then the number would be at 50%. Now, let's say you do high intensity cardio above the "fat burning zone" and you burn 750 calories, 300 of them being from fat. Catch my drift? the total amount of fat burned would be more, but more importantly, the total amount of calories burned would be more. Burning fat or carbs during workout doesn't really matter, because at the end of the day what matters is calories in vs calories out.
Now, to the OP:
Did you start from no exercise and going straight to HIIT 6 times a week? That's probably not such a good idea. If your body is not used to the stress from training, then you should ease into it. I know it sucks, but you can avoid many unecessary injuries this way.
As for losing fat and gaining muscle.. possible, but it's not a given that this will happen. It's usually very hard to do both at the same time and it is often recommended to focus on one or the other (that doesn't mean you have to go on a crazy bulk and gain lots of fat if you want to gain muscle though, like the traditional bulk, it just means that if you want to gain muscle you should eat slightly over your calorie maintenance level and when you're in a surplus, even though it is very little, losing fat is hard). However, it is typically seen to happen more in newbies for some reason.