How did the book behave when Harry Potter left it fall open in and Stone chapters 9-12?

The book you're referring to is the Diary of Tom Riddle, which Harry Potter finds in the abandoned Chamber of Secrets. It's not mentioned in the book that Harry left it open at any point in chapters 9-12.

The Diary is described as behaving oddly in chapter 11 when Harry opens it and writes in it. It seems to respond to his writing, encouraging him to confide in it and offering him a sense of understanding and companionship. This behavior is later revealed to be because the Diary is a Horcrux containing a part of Voldemort's soul, and it's using Harry's feelings of loneliness and isolation to manipulate him.

So, while the book doesn't "behave" in a noticeable way in chapters 9-12, it does start acting strangely in chapter 11.