The student pilot stated that an approach was made to runway 32 at the Mobile Downtown Airport, Mobile, Alabama (BFM). The student pilot flared the airplane causing it to balloon, and then allowed the airplane to sink down. The student pilot flared it again, and the stall warning horn went off momentarily. The student pilot eased the elevator slightly forward and the airplane landed roughly. According to the student pilot, the airplane landed with more weight on the right wheel than on the left. The airplane slowed down and the student pilot pulled back on the yoke to further slow the airplane down. At this point, the student pilot noticed roughness with the flight controls. The student pilot taxied to the downtown air center, and parked the airplane. According to the student pilot, there were no problems with the flight controls, and no problems with the airplane during the pre-flight inspection. Post-accident examination of the airplane revealed the flight surfaces were intact. The center section of the airframe, and firewall were buckled. Examination of the propeller revealed it was bent aft.