THE INSTRUCTOR (CFI) & STUDENT BGN PRACTICING TOUCH-&-GO (T&G) LNDGS. AT 1ST, RWY 31 WAS IN USE. AFTER THE 1ST T&G, THE CFI TOLD THE STUDENT TO CHG TO RWY 5 FOR MORE FAVORABLE WIND CONDS. AT ABT THAT TIME, A COLD FNT WAS MVG THRU THE AREA, A TSTM WAS ABT 5 MI NW OF THE ARPT, THE WX WAS GETTING WINDY & THE CFI NOTED LGT RAIN ON THE WINDSHIELD. DRG THE CLIMB AFTER THE 2ND T&G, THE CFI NOTED THE ACFT HAD STOPPED CLIMBING AT ABT 200' AGL & TOOK CTL OF THE ACFT. LATER, HE SAID THE AIRSPEED WAS ABT 60 TO 65 KTS (BUT THE AIRSPEED INDCR WAS CALIBRATED IN MPH). CONCERNED ABT PWR LINES AHD, HE TURNEDTHE ACFT. HE THEN NOTICED IT WAS DSCNDG RAPIDLY & THE SPEED WAS DWN TO '55 OR MAYBE EVEN 50, WITHOUT REALLY CHANGING THEPITCH ANGLE.' THE ACFT THEN BANKED LEFT & ENTERED A NOSE DWN ATTITUDE. IT CRASHED INTO TREES, 2 VEHICLES & THE GND, THENSLID INTO A MOBILE HOME. CHILD NR MOBILE HOME WAS FATALLY INJURED. CFI THOUGHT FLAPS WERE RETRACTED FOR TKOF, BUT THEY WERE FND EXTDD 15 DEG. CANNABINOIDS FND IN PLT'S URINE, BUT NONE FND IN HIS BLOOD; URINE/PENTOBARBITAL LVL, 0.40 MG/DL.