We ate at Beaches 'N Cream on our last trip, and were on the regular dining plan. So, to answer your questions :
Fries are included with the burgers/sandwiches. You can also substitute fruit for the fries ( my wife did ), and I think you might be able to substitute onion rings, but there may be an additional charge. We didn't order any, so I don't know.
All desserts except the Kitchen Sink are included on the dining plan. I know, because both the wife and I ordered the banana splits. Yummy !!
Be aware that B & C is a 1 Table Service credit cost, not a counter service.