Not sure about the carts, but we have used our AAA card at all the restaurants in the parks and most at City Walk. The only ones that don't are your high-end restaurants such as Emerils. We have used it in the big store in Universal also.
Yes...most places at each park and CityWalk will accept the AAA discount. Food carts don't usually accept discounts. Just make sure to show it everywhere you go.
Most places honored the AAA discount (when I remembered to ask). We shopped at NBA City, and a sovienir shirt was discounted, but the AAA discount did not apply to NBA licensed merchandise. If you order Butterbeer at 3 Broomsticks or Hogshead Inn you get the discount, but if you buy it at one of the carts in the street- no discount.
Put your AAA card IN FRONT OF your credit card to help you remember to use it.