I'll give some input and clarification if I can:
1. Calories stored in adipose tissue absolutely can be used to increase muscle mass. Muscle protein synthesis requires two primary ingredients: protein and calories. The protein (and some of the calories) will have to be eaten, but some of the calories can come from stored fat. This has been documented in controlled experiments many times, and I have experienced it myself, going from a soft 200 lbs to a fairly lean and muscular 200 lbs over the course of a year of heavy lifting. My weight never fluctuated more than +/- 5 lbs the whole time, but my BF% dropped from ~22% to ~12%. The more overweight you are, the easier this is to do. People who are already overweight don't need bulk cycles, but as you get very lean it may become more necessary (if muscle gain is your only goal). The thing to remember is that when you try to trim back down later, you may lose some of that muscle, so be careful. For most people, trying to stay at least moderately lean (15% BF for men) all the time is the best option. Slow and steady over the long haul...
2. "Theory has it that this is why, when a person sheds body fat, they often feel dreadful for a while – it’s the stored toxins being released."
There is no evidence that this is true, and I'm pretty confident that it can't be true. It just doesn't make sense biochemically. There is no reason that fat loss would lead to a release of toxins as they would be dissolved in the lipid, not bound directly to triglycerides as they are released.
3. "Adipose tissue also works to balance the endocrine system so if your hormones are out of whack – for whatever reason – adipose tissue might increase or decrease in order to bring the system back into balance, or homeostasis."
I know the endocrine system is terribly complicated (even for people who study it carefully), but don't be tempted into making statements like this. It is much too vague to really mean anything. Adipose tissue produces several of its own endocrine hormones, and responds to many others produced by other organs. Recent research has put together several small parts of the puzzle, but the whole system is nowhere near being completely understood.
4. The science might be complicated, but the answer is not: eat real food and lift heavy things. A steady diet of (good quality) meat, fish, eggs, vegetables, fruit and moderate starches for your gut, plus a diet of DLs, swings, squats, pull-ups and presses for your muscles is almost everything you need. Add in lots of walking (avoid sitting all day) and you are in good shape. Of course, other checklist items like sleep and avoiding emotional stress or important, but I hope obvious.