re: As with Fallujah.
First, how many al-Qaeda were there when Saddam was in power?
About the same number. They were just in other countries at the time, or in Northern Iraq, which, as I understand it, doesn't really count.
I really wish you'd broaden your sources. You are missing a lot of what's happening. Hint: Al Qaeda is doing a lot worse in the "hearts and minds" department than the U.S. is.