According to the pilot of a Lake 4-200 EP, he was conducting water landings to a lake. He completed two landings and was climbing the airplane for a third, when, about 200 feet above the water, he reduced power to simulate a "power out or reduced power landing." As the pilot "attempted to round out the glide for the landing," he could not arrest the descent, and the airplane landed hard. The pilot took off again, then made a precautionary water landing to a full stop. The airplane and engine appeared to be undamaged, so the pilot took off again and made two touch and go landings to another lake, followed by a full stop landing. At that point the engine sounded "rough," so the pilot taxied to shore. There, it was determined that a propeller blade tip was missing, that a propeller strike had occurred to the turtle top, and that the hull was taking on water. Mechanics later changed the propeller, and the airplane was deemed airworthy to fly to another location for further inspection. A few days later, structural damage was found to cross frames in the hull. Weather at a nearby airport, about the time of the hard landing, included clear skies and calm winds.