As for your struggles..
If you do low calorie AND low carb diet..it is hard to keep it going for long and it might be too strict for your body....something has to give if you don't feed your body's needs correctly. Maybe you need to have a good look at your diet and what you choose to eat and what you are aiming to achieve with your diet.
LCHF is good diet if you aiming to get your blood sugar levels under control....the amount of carbs you choose to eat will show in your readings...keeping protein intake adequate (note! too much protein can raise your blood sugars, FATs don't !) and feed you body's energy needs with fats/oil and you don't feel real hunger, temptations yes, but that is then down to your will power. How tight carb control you keep and eating just enough rest of the things for not feeling actual hunger will get you weight down too. Other than keeping eye on carb contents, you don't have to count calories or even aware of them. The main thing is finding the balance of enough fats that will keep you sated so you don't have to struggle with hunger.
Once you tummy gets used to lighter feeling and those hunger messages start to die down...you can then easily bring fasting into the picture..one will follow after other quite naturally.
Take time to get your basic diet right...eat correctly adjust your blood sugars and rest will follow..