you don't need a wand for potions... that was literally said by Snape in his first potion lesson in Canon: "There will be no foolish wand-waving or silly incantations in this class."
Too fast, the way you resolved it was okay but you moved on too fast, especially with the mother, she should feel more guilty and a bit of grief for it to be realistic
you should have made his hair turn white from blacking iut after killing his father….i assume it will turn white at some point cause the cover picture so thought it would have been good timing but i guess ill wait and see