Class 7 and Class 8 are weight ratings. 8 is heavier. Your f-350 is a class 3, my f-250 is a class 2.
The change from tandem axles to single rear axle has to do with weight, ride, and expense. Those four tires on the back, that are not needed for a toter, are really expensive.
A single axle truck has a capacity of about 60,000 lbs. usually. Figure that the tractor weighs around 18k (it varies), the trailer will weigh around 12k (it varies) and that means that you have about a 30k cargo weight. Probably enough to haul your dump truck, if you are not carryong any other weight.