I numbered your questions, so as to refer to them more easily.
(1) Yes, it seems that way. In fact, some people (especially women) can put on lean mass at the same time as they are burning fat.
(2) Don’t worry about your caloric intake. Add enough fat to your meals to satisfy your hunger. You should be able to go hours without hunger pangs. If you experience hunger, add more fat to your meals. This assures the body that it is getting enough energy, and that it doesn’t need to hoard fat or to reduce your metabolic rate. If you eat fat to satiety, your body will signal you when it’s had enough. For most people, this automatically results in eating a caloric deficit, but there is one study in the literature where a participant consumed something like 3,000 calories a day and still lost weight at the same rate as the other participants. So don’t be afraid of fat!
(3) If you are replacing your former carbs with fat and eating to satiety, you will find it very hard to eat a caloric excess. Dr. Phinney, in his standard lecture, comments that as his patients work down to their healthy weights, they unconsciously start adding more fat to their diet, because the body is contributing less stored fat towards meeting its energy needs. Once people are maintaining their weight, all their fat consumption comes from diet rather than stored fat. But again, he says, the key is to eat to satiety and let the body dictate how much energy it needs. Fat is wonderfully satisfying, so you are highly unlikely to overeat if you can hear your body’s signal that you’ve eaten enough. (There are people who have damaged their hormonal signaling mechanism, but fortunately most of us do not fall in that category.)