What can be done about bats getting under the curved tiles at the edge of the roof?
Any opening in the roof can provide an opportunity for bird or animal nesting. For problem intrusions such as this, I would start by contacting an exterminating or pest control company since they undoubtedly would have some experience with such things. The method used for closing off the openings would depend largely on the desired aesthetics. Many openings on tile roofs are closed with mortar or polyurethane foam although wood trim may also provide an effective barrier as well.