You can show your DVC member card to get discounts at some restaurants. However, the only way to get the Disney Dining Experience card (or whatever the new name is) is to be an AP holder or Florida resident.
Nope. You can purchase both from Guest Relations at the same time. I suggest doing it at DTD. I love my AP and DDE (TIW?) card.
You can also purchase an additional card at a discount ($25) for a family member who lives in the same house, but this is only useful if you plan on doing a lot of separate dining. That secondary card doesn't have to be purchased at the same time as the primary DDE/TIW card.