I will try to answer both your questions at the same time. first off worn belts can cause drive issues. the next thing to check is the engine drive pulley, and the variable drive pulley between the two belts will get a groove worn in them, and will cause the belt to slip. I have seen engine drive pulleys with a groove that actually cut all the way through the pulley.
The wide drive belt grips the variable pulley real well, but only runs on the inside part of the groove at the engine pulley. It is like running a 5/8 belt in a pulley designed for a 1/2 inch pulley.