PA31 LNDG FAI MISUNDERSTANDS ATC CLRNC; HAS CONFLICT WITH PA18; AND BOTH ACFT ARE INSTRUCTED TO CIRCLE.

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I WAS CLRED TO LAND ON L DOWNWIND RWY 1R. ALSO I ACKNOWLEDGED THAT I HAD B737 IN SIGHT 10 MI ON FINAL RWY 1L. CTLR DIDN'T SPECIFY TO LAND #2 AFTER B737 FOR OTHER RWY 1R. I ASSUMED THAT I COULD LAND SHORT FOR RWY 1R; BECAUSE I HAD B737 IN SIGHT AND APCH CLRED ME TO LAND RWY 1R AND NOT SPECIFY TFC SEQUENCING FOR LNDG. WHEN I TURNED TO BASE FOR A SHORT FINAL RWY 1R; IT CAME TO A CONFLICT SIT WITH SUPERCUB FOR A SKI-STRIP RWY 1R. THEN I WAS TOLD TO CIRCLE TO LAND FOR THE SAME RWY; AND SUPERCUB WAS CIRCLING IN A DIFFERENT DIRECTION TO LAND FOR THE SKI-STRIP. MY MISTAKE; THAT I ACCEPTED SHORT FINAL WITHOUT PERMISSION. EVEN TWR DIDN'T SPECIFY TFC PATTERN WITH OTHER TFC. IT WAS MY MISUNDERSTANDING SOMEHOW IN THAT TFC FLOW; I JUST THOUGHT THAT TWR WANTS TO DO SHORT FINAL BEFORE COMING B737 ON PARALLEL RWY 1L. AT THE SAME TIME I PAID ALL MY ATTN ON COMING B737 ON PARALLEL RWY 1L. THAT'S WHY I MISSED THE OTHER TFC; THAT CAME TO A SKI-STRIP. I THINK IT WAS NOT SO CLR ON APCH CLRNC AND THEN TWR; BUT I THINK I ACCEPT MY OWN RESPONSIBILITY FOR MY ACTION. I SUPPOSE TO CLARIFY AND CONFIRM MY CLRNC WITH THE TWR; OR APCH; BEFORE MAKING OWN DECISION; AND NEVER ACCEPT SHORT FINAL WITHOUT CONFIRMATION WITH THE TWR. (I ACCEPTED SHORT APCHS ALL THE TIME IN THE PAST.) IT WAS ONE ADDITIONAL REASON FOR ME TO BELIEVE THAT IS GOING TO BE ANOTHER ONE FOR ME!