Interesting start. One question. If "to cast a spell" Harry "had to understand what he was doing almost on a molecular level and how and why the results that he had wanted to happen would happen," how could he have as much control at 15 as he did at three (what understanding of how and why did he have then?)? And how would "just instinct and desperation" give him that necessary understanding on the (almost) molecular level? And why would he need to keep his emotions in check if understanding is crucial?
If a wand has more reaction for a muggle than for a mage, then why the Priori Incantatem effect with Voldemort's wand? You seem to indicate that his being a mage is an explanation for that ("It would certainly makes sense and explain why his wand was so useless to him, if not why it reacted the way it did when he dueled Voldemort in his fourth year.").