True.
True.
Untrue. Kinda. It depends on what and how you're eating. If you eat a lot of carbs, your body burns more carbs. If you eat more fat, your body burns more fat. Going low carb isn't necessarily more geared toward fat burning if you increase your fat intake. De novo lipogenesis (carbs to fat) is actually pretty rare, and requires that your body's glycogen stores be completely full already, and that you overeat on carbs by a significant amount for a few days.
Now, you will be burning less fat as you ingest carbs, so you may not necessarily be burning a lot of fat, but as far as it TURNING to fat, it's not really going to happen in a meaningful amount.
http://www.bodyrecomposition.com/nut...torage-qa.html
http://www.bodyrecomposition.com/nut...oxidation.html
True, but it's even rarer for a protein to turn to fat than it is for a carb to turn to fat, so you can pretty much ignore protein turning to fat in any meaningful amount.
False. Pudginess has nothing to do with protein intake. However, it will be hard to have much muscle definition without adequate protein intake and training. It's true that not exercising can be catabolic, but then, exercise is also catabolic. Losing weight of any kind, whether it's muscle or fat is catabolic, by definition. Catabolism is just breaking down body tissue for energy, whether that's fat or muscle. So, you could be catabolic and not exercise by taking in less calories than you burn. You could also be ANABOLIC and not exercising by taking in more calories than you burn and building up fat tissue. I think what we're concerned with in this thread is muscle catabolism/anabolism, and fat catabolism. Neither are necessarily connected to exercise (except muscle anabolism and resistance training).
The timing is absolutely irrelevant, but it's clearly working for you, so keep it up.