The pilot reported that during the night landing, he maintained a little more than normal speed and power since this was his first night landing at the McCarran Airport. He stated that on final approach for landing, heavy left rudder was needed. He stated he touched down on the left main, kept the nose up, and when he lowered the nose, the right wing went to the ground and the propeller dropped to the ground. Subsequently, the plane went off the right side of the runway and hit a ditch. During the investigation, all 3 gear were found in the gear wells, but the main gear doors were partially opened. The landing gear selector was found in the down position. The lock-out feature was not engaged. No discrepancies were found with the gear system, except that the warning horn was inoperative. When checked, the horn housing became hot and eventually deactivated the circuit breaker, which in turn, deactivated the gear position lights. The pilot did not recall seeing a safe gear indication.