A STUDENT PLT DISPATCHES HIMSELF TO AN UNAUTH ARPT OF OP AND RUNS OFF THE RWY DURING LNDG. ANOTHER ACFT'S INSTRUCTOR PLT LANDS; CHKS ACFT AND GOES WITH STUDENT PLT BACK TO HOME BASE. AGAIN; THE ACFT IS NOT INSPECTED BY A MECH AND THEN IS FLOWN IN TRAINING. CHIEF PLT STEPS DOWN FROM POS AT FLYING SCHOOL.

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STUDENT PLT WAS ON A SOLO FLT IN THE LCL PRACTICE AREA AND DECIDED THAT HE WOULD PRACTICE TKOFS AND LNDGS AT W66 WITHOUT A LOGBOOK ENDORSEMENT; BUT HE ALSO DIDN'T HAVE EITHER HIS MEDICAL OR LOGBOOK IN HIS POSSESSION AT THIS TIME. I MYSELF WAS ALREADY FLYING AT THE TIME WITH ANOTHER STUDENT AND I DID NOT DISPATCH HIM. ON THE LNDG ROLL THE STUDENT WENT OFF THE SIDE OF THE RWY IN WHICH HE THEN RETURNED THE ACFT BACK ONTO THE RWY AND SHUT DOWN. MY STUDENT CALLED ANOTHER INSTRUCTOR AND THEY BOTH DETERMINED THE AIRPLANE SAFE FOR FLT AND PROCEEDED BACK TO MANASSAS; VA. UPON THEIR ARR; I LECTURED STUDENT FOR EVEN FLYING IN THE FIRST PLACE AND THEN ADVISED HIM THAT WE WOULD NEED REMEDIAL TRAINING. AFTER THE STUDENT LEFT; THE AIRPLANE WAS DISPATCHED AGAIN WITHOUT BEING INSPECTED. THE FLT SCHOOL REQUIRES AN INSPECTION AS A 141 PROGRAM. AS A RESULT OF THIS MATTER; I STEPPED DOWN AS CHIEF PLT. I WAS NOT EVEN AROUND WHEN THE STUDENT WAS DISPATCHED OR WHEN THE INCIDENT OCCURRED IN WHICH THE AIRPLANE DID NOT RECEIVE ANY DAMAGE. SUPPLEMENTAL INFO FROM ACN 397947: FAILED TO RETRIEVE MY LOGBOOK AND MEDICAL FROM MY TRAINING FOLDER. AFTER DEP; I PROCEEDED TO THE PRACTICE AREA TO WORK ON MANEUVERS. AFTER THE MANEUVERS; I TRIED TO PERFORM A TOUCH-AND-GO AT AN ARPT I WASN'T SIGNED OFF TO GO TO. DURING THE ROLLOUT PHASE OF THE FLT; THE PLANE WAS BLOWN OFF THE L SIDE OF THE RWY AND ROLLED THROUGH THE SOFT GRASS AND MUD. I PROTECTED THE NOSE GEAR BY CONFIGURING THE ACFT FOR A SOFT FIELD LNDG. ONCE I SLOWED DOWN; I STEERED ONTO THE RWY THEN PROCEEDED VIA THE TXWY TO THE RUNUP AREA. HERE; I CONTACTED AN INSTRUCTOR WHO WAS IN THE AREA (MONITORING THE UNICOM). I SHOULD HAVE NOT GONE TO THE ARPT IN THE FIRST PLACE. I SHOULD HAVE NOT BEEN UNDER THE ASSUMPTION THAT I COULD. SUPPLEMENTAL INFO FROM ACN 397835: I WAS FLYING WITH A STUDENT NEARBY AND HEARD ON THE RADIO THAT THE SOLO PLT WANTED ME TO LOOK AT THE ACFT. WHEN I GOT TO W66 THE PLANE WAS ON THE TXWY AND APPEARED IN GOOD CONDITION. I SENT MY OWN STUDENT (PROPERLY ENDORSED) BACK TO OUR HOME BASE OF HEF (MANASSAS; VA) AND RETURNED HOME IN THE SOLO STUDENT'S ACFT WITH HIM. MAINT INSPECTED THE ACFT AND FOUND NO DAMAGE THAT WOULD CAUSE AN UNSAFE CONDITION. APPARENTLY THE ACFT HAD BEEN IN AN 'UNUSUAL' SIT BY EXITING THE HARD SURFACED RWY AND WAS NOT TO BE FLOWN WITHOUT A CERTIFIED MECH LOOKING AT THE ACFT.