to take the temp put a thermometer in the return grill and put on in the closest supply grill.
Yes duct work that is too small will also cause condensation, as well as other problems. The reason to have the stat set for auto is so after the cooling cycle it has a chance to dump all remaining condensation off of the coil and allow it to also drain out of the drain pan. if water is allowed to stay on the coil or in the pan it will put humidity back INTO the house.
Again if the ducts are not insulated and the humidity is high in the basement they will sweat. open up some of the grills in the basement to help it move some air around and allow air from the basement to get to a return (if there isn't one in the basement) so that it can help pull the humidity out.