POTENTIAL CONFLICTS AND SIMULTANEOUS XMISSIONS AT A NON FEDERAL FACILITY. TWR CTLR HAS PROBS MANAGING THE TFC VOLUME AT FMN; NM.

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XMISSION TO TWR BLOCKED BY ANOTHER ACFT CALLING FMN TWR AT THE SAME TIME DURING RPT OVER FMN VOR. PROC TURN INBOUND; CLRNC FOR THE VOR RWY 25 APCH AND MISSED APCH HAD BEEN XMITTED AND ACKNOWLEDGED. THE CTLR STATED THE FMN VOR RPT WAS NEVER RECEIVED. I HAD IN FACT RPTED XING THE FMN VOR. THIS WAS SUPPORTED BY MY INSTRUCTOR WHO INFORMED THE TWR THAT FMN VOR WAS RPTED. A REVIEW OF THE TWR TAPE INDICATES A XMISSION AT THIS TIME WAS BLOCKED BY ANOTHER ACFT CALLING TWR AT THE SAME TIME. DURING THIS TIME THE CTLR SEEMED OVERWHELMED. SHE REPEATEDLY ASKED ACFT IN THE VICINITY OF FMN ARPT FOR THEIR LOCATION; ALT; AND HDG. SHE STATED; IN AN IRATE MANNER; THAT SHE COULD NOT SEE THEM -- SHE ONLY HAD BINOCULARS. TO AVOID TFC CONFLICTS; WE EXECUTED AND CALLED A MISSED APCH APPROX 3 MI FROM THE RWY AT 6500 FT MSL (MDA IS 6060 FT); WHILE MAINTAINING VISUAL CONTACT AND SEPARATION FROM OTHER ACFT IN THE VICINITY OF THE ARPT. DURING THE SAME FLT; WHILE PRACTICING APCHS UNDER THE HOOD AT FMN ON SHORT FINAL TO THE VOR DME RWY 7 APCH; A BEECHCRAFT BONANZA WAS TURNED IN FRONT OF OUR BEECHCRAFT BARON BY ATC. APPROX 1500 FT HORIZ SEPARATION AND NO VERT SEPARATION EXISTED AT THIS TIME. EVASIVE ACTIONS WERE DEEMED NECESSARY BY MY INSTRUCTOR TO AVOID OVERTAKING THE SINGLE ENG ACFT. A DISCUSSION FOLLOWED WITH THE DESIGNATED EXAMINER WHO WAS ON BOARD THE BONANZA. HE HAD INSTRUCTED HIS APPLICANT TO INCREASE PWR AS WE HAD REDUCED PWR TO AVOID CLOSURE BTWN THE 2 ACFT.