A C172 PILOT REPORTS A NMAC AFTER A HEAVILY FOREIGN ACCENTED PA28 PILOT REPORTED INCORRECT TFC ON FINAL IN SIGHT AND TURNED ON TOP OF HIS ACFT.

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I WAS INVOLVED IN AN NMAC WHILE ON AN INSTRUCTIONAL FLT. WE WERE PRACTICING VISUAL APCHS AND LNDGS. ON APPROX THE THIRD OR FOURTH APCH; AN ACFT CALLED INBOUND FROM ZZZ ARPT. THE PLT WAS VERY DIFFICULT TO UNDERSTAND AS HE DID HAVE AN EXTREMELY STRONG ACCENT. HE WAS INSTRUCTED TO ENTER R DOWNWIND; AND RPT MIDFIELD FOR RWY 22. THE PIPER PLT THEN REPLIED HE WOULD ENTER R DOWNWIND RWY 22 WHICH AGAIN WAS HARD TO UNDERSTAND. AS WE APCHED THE MIDFIELD ON APPROX OUR THIRD OR FOURTH APCH WE GAVE OUR POS RPT AND REQUESTED THE OPTION. AS WE DID THAT; WE WERE INSTRUCTED TO FOLLOW TFC AHEAD OF US ON THE DOWNWIND. ONCE WE RPTED TFC IN SIGHT; WE WERE THEN CLRED FOR THE OPTION. AS WE WERE CLRED FOR THE OPTION; THE PIPER PLT RPTED MIDFIELD; AND THEY WERE INSTRUCTED THAT THEY WERE #3 FOR THE RWY AND TO FOLLOW THE SECOND CESSNA ON DOWNWIND; AND THE PIPER PLT RPTED TFC IN SIGHT. TWR THEN ASKED IF THEY HAD THE SECOND CESSNA ON DOWNWIND IN SIGHT (TWR PLACED THE EMPHASIS ON SECOND) AND THE PIPER PLT REPLIED THAT THEY HAD THE SECOND CESSNA IN SIGHT; AGAIN THE ACCENT MADE IT VERY DIFFICULT TO UNDERSTAND. THE PIPER PLT WAS THEN CLRED TO LAND FROM THERE. WE EXTENDED OUR DOWNWIND TO ALLOW FOR SPACING SINCE OUR TFC WAS A FULL STOP. AS WE APCHED OUR BASE TURN APPROX 1 1/2 - 2 MI FROM THE RWY AT 1000 FT; THE PIPER PLT ALMOST DSNDED ON TOP OF US; COMING WITHIN 3 FT OF OUR ACFT. WE THEN HAD TO DO AN EXTREME DSNDING TURN TO THE R. THEN THE PIPER PLT BEGAN TO TURN TO THE R AND JOIN THE FINAL. ONCE WE WERE STABILIZED AND A SAFE DISTANCE FROM THE PIPER AND NO LONGER ON A COLLISION COURSE; I HAD ADVISED ATC OF THE SITUATION AND STATED THAT I WANTED TO FILE AN NMAC RPT. THEN THE PIPER PLT SAID THEY HAD THEIR TFC IN SIGHT ON FINAL TO THEIR R. WE THEN CONTINUED WITH THE APCH BUT BECAUSE OF THE MANEUVER; THE ACFT AHEAD OF US (OUR TFC TO FOLLOW) WASN'T OFF THE RWY YET SO WE HAD TO GO AROUND. WE THEN WERE INSTRUCTED TO MAKE L TFC FOR RWY 22; WHICH I WAS GOING TO REQUEST TO REMAIN CLR OF THE PIPER BECAUSE THEY HAD TO DO A GAR AS WELL. WE FLEW OUR L PATTERN AND THEN LANDED WITHOUT ANY FURTHER ISSUES.