Hey there - sorry for the slight delay getting here! Reviewing stories with multiple chapters takes me a while, and I'm pretty busy at the moment - but I'm here now ;)
First off, I have to say that I absolutely lovelovelove the idea for this! The idea of magic just vanishing, or being used up or destroyed, the whole magical world collapsing, and a dystopian-like world in the aftermath? A Potter/Weasley family conflict, and two geniuses with competing interests, etc.? Yes, please! It's got all the ingredients for a fabulous story - seriously! :)
I really like the fact that Rose and Albus are the main characters, as well, even though they're often used, is so good because even without reading it I can tell you're going to take them in completely unique directions. So far, I like what you've shown us of Rose. I love her adoration of her brother, the fact that she cares about him enough to mess around with magic no one's seen before, and the way she simply accepts her situation. She knows the score; she doesn't care, because it doesn't matter. It's a lovely selfish/not-selfish, confident paradoxical sort of thing. It's great!
A couple of quick grammary-type things! First, I know you've got huge spaces between sections, but maybe use a line instead? There's a function on the editing screen when you submit your chapter to add a horizontal line, which would look cleaner and get rid of white space ;) Also, in dialogue it should end: 'Completely,' she said.', for example, rather than 'Completely.' She said. Easy enough to change!
More difficult... You tend to use short sentences, rather than linking them together. For example, here you said 'At its core though, magic isn't just a collection of spells. It's not a compilation of potion ingredients. It's not the stream of light that comes out the end of a First Year's shaky wand.', which would sound better linked together, using 'or' and commas. It would just help the flow ;) Another quick thing - try not to repeat things too often, unless it's meant to be stylistic or in a list: you repeated 'the man on the left' a lot in one paragraph and it sounded a bit odd to me.
I love the sections and the style, and the glimpses of future/past that we get. It's a really interesting way to write, and I'm really curious about what happens. I also really like the Head Auror - how it's not Harry, how he's plotting Kingsley's downfall, how he's ambitious and thinks she could help him... he's a really good character and adds to the sense of mystery you've established with this about what happens to rid the world of magic.
Really, really good start; lovely characters, brilliant plot, nice style, pace, etc. I really don't think there's anything that would deter a reader, so you're all good! :) Feel free to re-request!
Author's Response: Wow, thanks for the kind review. I'll fix the dialogue tags and add horizontal lining. I've actually tried to do the lines but for some reason they don't work for certain chapters. Some of the sentence decisions were intentional and meant to convey a certain tone. I don't think I'll be changing them in this chapter but I will keep what you say in mind in the future! It's just that this chapter was written so long ago and with every chapter I feel my writing style changes regardless so...
Thanks for the constructive criticism and kind review! I appreciate it :)