Your AP will expire one year from the day you actually pick it up at WDW.
And yes, when you order the AP, they will send you a voucher for it. You can then call and purchase the DDE using the numbers on the AP voucher. But I think you have to have that voucher actually in your hand when you purchase the DDE.
The DDE is supposed to be a one-year card, but I think they have been making them 13 months from the manufacture date of the cards. So some clever folks have been ordering the DDE at the last minute, getting an emailed or faxed confirmation of the DDE, and then using that document on their first trip. Then, when they get home, they receive a DDE card which has 13 more months left on it. That might or might not be important, depending on when you were planning to visit on subsequent trips.