Your body makes no distinction between types of training. Body weight work, dumbbells, and bands are all capable of building muscle. This is because the body perceives muscular tension as being the same no matter what the source of that tension is. The level of tension that can be achieved can vary obviously, with dumbbells and bands having an easier route to higher tension. However, body weight work usually requires variations on exercises in order to increase the tension to a desirable level (after building sufficient muscle in the basic version of an exercise). Because of this, body weight work can be a bit confusing to beginners. Regardless, any muscle that can be trained with weights or bands can be trained doing body weight work. The simple truth is that one of the three mentioned methods of training will usually be more efficient than the other two for reaching certain goals, and your goals will determine which method you'll want to utilize (sometimes all three).
You mention fat loss here, but I believe that you're looking at this the wrong way. Exercise does many things, but two things in particular that most people are concerned with are that it builds muscle and burns calories. The amount of calories that can be burned through exercise pails in comparison to what can be achieved with a proper diet. If fat loss is your goal, you should be focusing on your diet first. Exercise is a fantastic thing, but your diet will determine how much fat you gain or lose, not your style of exercise.
Okay, that said, let's now address your questions specifically...
Can bodyweight exercises induce body recomposition?
Yes, but so can any type of exercise that stimulates the body properly.
Could performing bodyweight exercises (with added weight when necessary) induce fat loss more when compared to similar non-bodyweight based exercise?
It depends entirely on the exertion given and how much demand is being made on the muscles. The more you exert yourself, the more calories you will burn. You'll also create the opportunity for hypertrophy, which in itself burns calories. Therefore, the harder the work, the more fat loss you will see from it. I should reiterate that your diet will be the primary concern here however.
Could focusing on exercises which are sensitive to (affected by) one's own bodyweight induce the body to adapt its power to weight ratio?
Yes, but again, so could any type of training. The reason being is that the muscles will get bigger and stronger from training.
Has this been tested or studied scientifically?
Yes. To be blunt, this is the entire purpose of strength training.