With the regular Disney Visa card, you earn 1% in points for each purchase. Anywhere. To redeem points you do need to transfer them to a Rewards Redemption Card -- similar to a gift card but not the same, one big difference is redemption cards have an expiration date. The Premier card earns 2% rewards for purchases at gas stations, grocery stores, restaurants, and Disney; and 1% on everything else. Points are redeemed the same way, except with the additional option of using points for airline tickets.
There are standard offers, such as 0% interest on vacation packages purchased through Disney Travel, shopping/dining discounts, the Character Spot picture from Epcot, etc. There are also occasional special offers such as broadway shows, pins, etc.
SOME offers from WDW (free dining, room-discount, etc.) are available to Disney Visa cardholders for maybe up to a week prior to releasing the same offer to the general public; but the advanced notice isn't always available.