AFTER LEVELING AT FL330, THE #2 ENG FIRE WARNING LIGHT & BELL ACTIVATED. THE CREW FOLLOWED THE PUBLISHED PROCEDURES, SHUT DOWN THE ENG & USED A FIRE BOTTLE. THEY THEN DIVERTED TO CINCINNATI & MADE A PRECAUTIONARY LANDING. AFTER LANDING, FIRE DEPT PERSONNEL MONITORED THE ACFT & RADIOED INFO TO GROUND CONTROL. IN TURN, GROUND CONTROL RELAYED INFO TO THE CREW WHILE TAXIING. FIRE TRUCK PERSONNEL REPORTED SEEING A 'SMALL AMOUNT' OF SMOKE FROM THE #1 ENG. GROUND CONTROL RELAYED THE INFO WITHOUT THE WORDS 'SMALL AMOUNT.' SUBEQUENTLY, THE ACFT WAS STOPPED & WAS EVACUATED USING THE ESCAPE SLIDES. 1 PASSENGER WAS SERIOUSLY INJURED WHEN A SLIDE BURST. THERE WAS EVIDENCE IT WAS PUNCTURED BY A SHOE NAIL AFTER THE SHOE'S HEEL CAME OFF. INVESTIGATION REVEALED THERE WAS A FALSE FIRE WARNING INDICATION DUE TO A SHORTED FIRE DETECTOR. THE FLT ATTENDANTS (F/A) WERE NOT PROPERLY BRIEFED. 1 F/A UNHOOKED A GIRT BAR BEFORE OPENING EXIT 4R, RENDERING IT UNUSABLE. SOME PASSENGERS TRIED TO EXIT WITH CARRY-ON BAGGAGE. THE REAR STAIR EXIT WAS NOT USED.