The student pilot reported that he conducted multiple full stop landings. During the last landing, as he flared the airplane, it landed hard and bounced on the runway multiple times. As the student pilot attempted to regain control of the airplane, the propeller contacted the runway and the nose wheel buckled before the airplane came to a full stop. An examination of the airplane revealed substantial damage to the firewall and engine mounts. The student pilot reported that there were no mechanical malfunctions or failures of the airplane that would have precluded normal operation.