While on the diet you body uses ketones produced from fat instead of carbs for energy leading your body to be in a metabolic state called ketosis. This makes your body highly efficient at burning fat that you eat, but also fat that is stored in your body leading to drastic reductions in weight over short periods of time.
Distance running can look daunting if you have not exercised in years. Cardio stamina takes time to develop, and the key to building more as with anything is regular practice. Start by signing up for a race and get someone to join you.