When I went the first few days we ran a mile or two, but during mock sea trials we ran a total of 8-10 miles throughout the day. Then the last morning we went on a 3 mile run. A fair amount but it wasn't terrible.
The CFA you take at NASS DOES count for your application, but you can retake it if you feel you can do better. Would recommend that course of action if you do poorly but well enough to pass.