The headaches and nausea, the “keto flu,” are caused by low sodium intake. Eating carbohydrate causes the body to retain sodium and water, so once we essentially eliminate carbohydrate from our diet, we need to work a bit to keep sodium up and stay hydrated. (Not only that, but we all need more salt than the current U.S. government recommendations suggest.)
Keeping carbohydrate under 20 g/day allows insulin levels to fall and thus permit the metabolism to normalize and any excess fat to be metabolized.
Keeping protein moderate, i.e., somewhere around a gram a day per kilo of lean body mass, keeps the body from eating its muscle mass (if too low) and from stimulating insulin production (if too high).
Eating fat to satiety allows the body to decide when we have given it enough energy to do its job (and it barely stimulates insulin secretion at all, in the process). Consciously restricting calories is not a good idea, because if we set the level too low, the body has to reduce its metabolic rate to compensate; if we set it too high, it needs to find ways to get rid of the extra energy.
Insulin blocks the leptin generated by the adipose tissue, which is supposed to tell the brain we don’t need to eat, from registering. A few weeks of low-carb is often all it takes for the brain to start “seeing” the leptin signal again, and after an initial period of high appetite, the appetite settles down to a reasonable level—all without conscious effort on our part.
Women often find that they have an odd response to starting a ketogenic diet. Gaining weight in the beginning is not completely unheard-of. Women who have restricted their calories for some time often find that the body wants to put on lean muscle tissue, even while shedding excess fat. This confuses the scale, but since muscle is denser than adipose tissue, your measurements can still shrink from losing fat, regardless of what the scale does. You have to decide whether an absolute number from the scale trumps being fitter and leaner, or not. (We recommend the latter, of course.)
Women also find that their weight fluctuates with their hormones. The time of month makes a big difference, from what I understand. Also, where a woman is in her reproductive life also has an enormous influence. The upshot is that women generally have quite a different weight-loss journey from what men have.