I'll second JDE's comment - this story gets better as it goes along.
I've seen other stories that use a similar plot device in which Harry is trained elsewhere and comes to Hogwarts with a mission to kill Voldemort and annoy Dumbledore. This story stands out among those, I think, because your Harry has such a well-developed personality; he can radiate badassery when he needs to, but he can also be friendly, polite, and gentle, and even a bit of a sexual innocent. That makes him a lot more fun to read than if he were a one-dimensional Super!Harry.
I like your Hermione and Neville too, for similar reasons. I want to like Susan, but we haven't seen as much depth from her yet. I hope you'll give her more screen time soon.
Your chapters start and end in good places, and there's very little waste in between. I'd say they're just the right length.
Thanks for writing! I'm looking forward to more.