Does dry eyes cause pain in the eyes?

Yes. Dry eyes can be painful. It is important to keep your eyes well lubricated.
Yes. Adequate tears are necessary to lubricate the top layer of the cornea, the clear dome over the fron of your eye and the conjunctiva, the "skin" over your eye ball. When they are insufficient, small defects can occur in the top layer, exposung nerves underneath- and this causes discomfort, sandy or gritty feeling and pain.