According to the student pilot, during landing on his solo flight the airplane porpoised. He reported that after landing he repositioned the airplane, but prior to takeoff, a fellow pilot, who witnessed the porpoise, contacted him on the VHF radio, and informed him that he should have the airplane checked out before attempting to takeoff. The student pilot taxied to the parking area and the airport manager and airframe and powerplant mechanic inspected the airplane. The student pilot called his flight instructor and conveyed the situation and the level of damage. However, according to the flight instructor, the student pilot only conveyed the damage to the tail skid. The flight instructor reported that he told the student to confer with the mechanic and determine if the airplane was airworthy. The student pilot departed and proceeded to the airport where his flight school was based. Shortly after the departure, the airport manager that looked the airplane over for the student pilot, called the flight school and conveyed the gravity of the situation and informed the school that the airplane actually sustained damage to the firewall, tail skid and rudder fairing. The flight instructor did not confer with anyone other than the student pilot to ensure the airplane was airworthy. The airplane sustained substantial damage to the fire wall. The student pilot reported that there were no mechanical failures or anomalies with the airplane prior to or during the flight that would have prevented normal flight operation.