The student pilot reported that, during his solo cross-country flight, he performed touch-and-go landings and takeoffs. The student pilot reported that there was a notice to airman identifying that the precision approach path indicator (PAPI) lighting was not in service at the second of three airports on his itinerary. The student pilot was cleared for a touch-and-go at the airport with no PAPI, and he reported that his landing was flat. He recalled that the airplane bounced but that he completed the touch-and-go and departed the airport for the final leg of his itinerary. He reported that he landed and shut down the airplane at his home airport, and "it was then that I noticed the bent prop tips. I immediately notified management." Further examination of the airplane by the operator revealed substantial damage to the firewall. The pilot reported that there were no preaccident mechanical malfunctions or failures with the airplane that would have precluded normal operation.