Your metabolic rate increases when you are awake, because suddenly it has a whole body to deliver oxygen and nutrients to. When you're asleep your body is ticking over, taking care of repairs while your engine idles.
Awake, you move around, you use more energy even if just sitting in a chair. Your brain is active (and the brain burns a LOT of energy), your muscles are active, your heartrate is increased, and so on.
Breakfast doesn't so much "kick-start" your metabolism as kick-start your digestive processes. Taking energy from digestion is faster than taking it from fat storage, so breakfast gives you a kick-start feeling because it lifts your blood sugar levels more quickly than just relying on body fat will.
Realistically to lose weight you need energy from fat stores and energy from food. Food keeps you ticking over in the short term, and gives you the energy to pull fat out of storage ('cause, yes, that takes energy).
If you start starving, taking energy from your muscles is easier than taking it from fat storage. Lovely! Yes, your body will basically "eat" your muscles rather than starve