Harry knows because Lash absorbed the book and transferred it to Harry's mind. If it was so easy to remember, why would Kemmler write it down for anyone to use when he could just memorize it, and keep that powerful knowledge for himself?
Because Kemmler wanted to spread his knowledge as was specifically stated in dead beat. It took the council a lot of effort to burn them. This was not a private journal with critic notes, this was a manual for people who came after him. Just like his other books.
And also as a way to create more problems for the council of course.
But I think Grevaine also said something like this when he took the book from Harry.
