The private pilot reported that he was performing a water touch-and-go landing on a river, about three miles from the departure airport. He also reported that he was distracted by potential skydivers, towers in the area, and by discussing the route of flight with his passenger. He did not retract the landing gear following the previous runway takeoff, and landed the amphibious airplane on the water with the wheels extended. The airplane immediately nosed over and came to rest inverted in the water. The pilot reported that the fuselage and wings sustained structural damage. He did not report any pre-impact mechanical malfunctions or failures with the airplane that would have precluded normal operation.