One minor note -- sorry it's not a real review. In canon, Dippet was still alive at the point you have Harry start talking to his portrait.
Since you will no doubt have readers even more obsessive than me, you might want to explain that one way or the other. E.g., say why there was a portrait of a living person and assert that it was possible, or change it to a different headmaster. Or just have Harry exchange letters with Dippet directly.
Author's response
Wrong. Dippet died in late 1992, which could be considered Oct-Dec. Since the Chamber was opened on Halloween, if Dippet had died in say early November, then it would have been entirely plausible if Harry had done so after that fact. But since I know there are serious uber fanatics about things like this, just to be a compete dick, Armando Dippet died on October 31, 1992, at the exact same time as Mrs. Norris became petrified.
Besides, no one ever said the person had to be dead for the portrait to activate. They could activate as soon as their likenesses tenure as Hogwarts Head ends. It could entirely be a coincidence that all of the other Headmasters and Headmistresses tenure ended by death, and Dippet is the only one who'd actually gotten the chance to actually retire.