You don’t need endurance exercise to burn fat.
The idea is that weight training can lead to an increased metabolism for a few days, while endurance exercise only revs up your metabolism for a few hours after you are done working out. If you work out hard enough in the gym and eat properly afterwards, then you will have no trouble losing weight.
I can not really comment on this. I agree that after a really tough workout in the gym I tend to be really hungry afterwards, but I am also really hungry after a tough running workout. My regimen usually includes a fairly balanced mix of weight lifting and running, and the only problems that I have controlling my weight are making sure that I eat enough to not waste away.