A BE10 MAKES AN APCH TO THE WRONG RWY AT FRG; NY. FLC EXECUTES A GAR AND HAS A LESS SEVERE NMAC WITH AN SMA.

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SHORT REPOS FLT FROM HPN-FRG (20 NM). RECEIVED VFR ADVISORIES FROM ZNY. ZNY CANCELED RADAR SVC 6 NM FROM FRG AND TOLD US TO CONTACT TWR. PATTERN WAS EXTREMELY BUSY WITH SINGLE ENG; TOUCH-AND-GO TFC. UNABLE TO ESTABLISH CONTACT WITH TWR; I ORBITED 6 MI S OF CLASS D AIRSPACE. AFTER ABOUT 4 MINS OF ORBITING; CTLR CLRED US TO RWY 19 AND TO RPT WHEN PASSING OVER A SHOPPING MALL. BY NOW IT WAS APPARENT THAT THE CTLR WAS HAVING DIFFICULTY GETTING THESE TRAINING ACFT TO FOLLOW HIS INSTRUCTIONS. THIS INVOLVED EXTREME USE OF THE FREQ; AND WE WERE UNABLE TO CALL OUR RPTING POINT. DURING THIS CONFUSION; I LINED THE ACFT UP TO LAND ON RWY 14; RATHER THAN RWY 19; AS INSTRUCTED. BY NOW; THE CTLR WAS SO OVERWHELMED THAT HE CLRED US TO LAND ON RWY 19; BUT I WAS LINED UP TO RWY 14; THINKING THAT I WAS ON RWY 19. ON APPROX A 1/2 MI FINAL; I REALIZED MY ERROR AND EXECUTED A GAR. WE SAW AND AVOIDED A PA28 THAT HAD GONE AROUND ON RWY 19. (WHY; I DO NOT KNOW.) ON THE GAR; WE ADVISED TWR AND REQUESTED L DOWNWIND TO RWY 19. HE (TWR) SEQUENCED US #2 FOLLOWING TFC ON THE R DOWNWIND. AFTER APPROX 1 MIN OF SEARCHING; I SAW A SINGLE ON 1/2 MI FINAL AND BELIEVED THAT TO BE MY SEQUENCE. WE COULD NOT CONFIRM DUE TO EXTREME RADIO CLUTTER. AS I COMPLETED MY BASE TURN; TWR TOLD US NOT TO START BASE BECAUSE OUR SEQUENCE WAS JUST TURNING FINAL OUTSIDE US. I MANEUVERED THE ACFT BEHIND HIM AND SLOWED AS MUCH AS POSSIBLE. IT BECAME APPARENT TO ME THAT THE SPACING WAS INADEQUATE AND ASKED PNF TO REQUEST A 360 DEG TURN ON FINAL. WE WERE STEPPED ON TWICE AND UNABLE TO ESTABLISH CONTACT; SO I EXECUTED THE 360 DEG TURN ANYWAY; CAREFULLY SEARCHING FOR TFC. UNEVENTFUL LNDG WAS MADE ON RWY 19 AND TWR MADE NO COMMENT. MISTAKES; IN ORDER OF IMPORTANCE: 1) ME AND PNF FOR LINING UP ON WRONG RWY -- VERY UNPROFESSIONAL. 2) TWR CTLR; FOR LETTING HIMSELF BECOME OVERLOADED. AT TIMES; HE WAS UNAWARE OF WHICH ACFT WAS WHICH. HE CLRED US TO LAND ON RWY 19 AT FIRST; AND NEVER SAW OUR MISTAKE OF LINING UP FOR RWY 14. 3) NEW YORK APCH FOR 'CUTTING US LOOSE' SO CLOSE TO THE FIELD. THIS IS A COMMON PROC AT FRG; AND MAKES IT DIFFICULT FOR BOTH THE FLCS AND THE TWR CTLR. THIS IS A CLASSIC EXAMPLE OF THE 'DOMINO THEORY' WHICH LEADS TO INCIDENTS/ACCIDENTS.