Some of them. Here's the information I've collected, from a variety of news articles. (The articles are often unclear on when the tickets were reserved vs. when they were paid for.)
On 8/25/2001, Atta set up an American Airlines frequent flyer account (#6H26L04).
On 8/28, Atta booked one-way tickets for himself and apparently also for Abdulaziz Alomari on AA flight #11 for 9/11. He paid with a Visa card, used his frequent flyer account, and gave the phone number 915-815-3004. This was on the American Airlines web site. He is said to have paid $4600 for the first-class ticket(s) (just his, or his and Alomari's, I don't know which).
On 8/29, Ahmed Alghamdi and Hamza Alghamdi purchased adjacent business class seats for $1760 each on United #175, also on the web. Mohad Alshehri bought a $4500 first-class ticket (on the same date, I think) for his flight. Fayez Banihammad also reserved his ticket on that date.
On the morning of 9/11, Atta and Alomari bought their tickets in Portland, ME, 17 minutes before the flight left. (They flew to Boston to catch the flight that they hijacked.) Some reports indicate that they bought tickets for Portland-Boston-LA, rather than just Portland-Boston; it's not clear how this squares with the reported 8/28 Visa purchase. Possibly Atta had guaranteed the 8/28 purchase with a Visa card, but paid cash instead at the airport? Or maybe the last-minute 9/11 purchase was really just for the initial Portland-Boston leg.)
Purchasing tickets two weeks prior, they were relying on a long-range weather forecast. The odds would doubtless be strongly in favor of good visibility in the Northeast quarter at this time of year.
Clear skies would have been an absolutely essential ingredient in their plan. Any overcast or storm clouds would have endangered the mission.
I'm inclined to discount the idea that 9/11 was a date certain from the outset of planning. Instead, they had a timeframe and a launch window...and the 9/11 date was circumstantial.