Q: will doing moderate to heavy cardio AND weight training increase fat loss IF there is no calorie deficit? My trainer tells me that it is best to mix the two, but according to your site, it isn't... is this because my trainer is assuming I will intake a lot of food?

A: By definition calorie deficit means you are losing weight, so if you don't have a calorie deficit, then you are maintaining your current weight which will always mean relateively slow body composition changes or even none at all. So calorie deficit is definitely needed for effective fat loss. Now, given that you are in the calorie deficit, I would not recommend the heavy cardio/heavy weights approach because it will lead to overtraining in most people. If you are an athelete or at least a well-conditioned young man, then it may work well for you, but for most it would lead to subpar results and eventual injuries because their bodies will be under too much stress and without sufficient time to recover from workouts and be under calorie deficit to boot. But even without the calorie deficit I would not recommend this for most people.

If you do decide to follow such a strenuous program, I very strongly recommend not continuing it for more than 6-8 weeks, taking a week's break from exercising at the end of that period, and then coming back to a less stressful program.