The money is essentially a hotel room discount, pay full price, get a rebate. Since Disney does not profit in the same way from DVC, as we pay for our room with points, whioch should alreay give us a substantial discount over the cash price of a room (else why would we have purchased?) there is no hitge anount of profit to rebate on the card.
If you do the math, you'll see it is no different that what the "Free" dining plans were. It really isn't free.
Of course you can. As long as you book a room for cash and not using points.
The dining card is effectively a cashback discount over rack rates, so it's valid only for cash bookings. As a DVC member if you use your points you don't pay cash so you don't get the discount. But being a DVC member doesn't stop you to pay the overinflated rack rates and get a small discount in the form of a gift card. Using your points you get a much higher savings than any discount Disney will ever come up with.