My outside heat pupmp still runs when the tstat is turned to off, have to shut it off at the breaker

Sounds like a bad tstat. What if you remove the faceplate of tstat?

may be a bad tstat. turn power off. put red green and yellow together inside stat. turn power on. if machine runs and cools, and stays cooling you need a new tstat. this is bypassing the tstat, nothing will turn your air off except the breaker. dont leave it this way.

has this tstat worked the heat pump before? possible refrigerant issues

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When you say door are you referring to the front door or the furnace door? If the unit kicks on AND off by itself I would say it's in the tstat or the tstat wire. If it were internal I would think the blower relay or heat contactor/relay were getting stuck AND THE FAN WOULD NOT TURN OFF until you flipped the breaker. Good luck

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Turn breaker off. Wire nut the red, green and yellow. Turn breaker on. Check outside. If unit is running either your tstat is not setup properly or it is bad

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There probably isn't a reset button=magic fix. With it in heat pump mode and tstat set above indoor temp, check your outdoor unit to see if it's operating. If not, check all breakers to it. Can you see any ice accumulated on the outdoor unit? If it is running and not producing heat, turn the tstat to emergency/auxiliary heat. and the heat pump turned off to prevent damage. You'll need a service tech.

get a new thermostat

Hello I would add a HARD START KIT to the run capasitor (if there is not one already).This makes the compressor come on easy.If the breaker trips during running time the pressures are too high,hose off the condenser coil (fins).The unit might be slightly overcharged but I would be careful before adjusting the freon at all.

OUTSIDE FAN OR INSIDE FAN OR BOTH. IF BOTH CHECK THERMOSTAT WIRE HOOK UP. IF YOU INSTALLED NEW TSTAT CHECK FOR JUMPER ON RH-RC TERMINALS ON TSTAT BACK PLATE. IF INSIDE FAN COMES ON WITH FAN IN ON SETTING AT FAN ON AUTO LEVER THAN PROBLEM IS AT OUTSIDE UNIT. CHECK FUSES IN BOX ON OUTSIDE WALL. SHUT OFF BREAKER FIRST.

Check your wiring between the contactor and compressor for a short to ground, or check the compressor windings for short to ground.
With the Tstat off, the contactor should be open so the only way for the compressor to be trying to do anything is if the 110 volts from the unbroken side are traveling through the compressor to ground. Since 110v is not enough to run it, the overload is kicking it out, cooling off, and repeating the cycle. When you kick on the Tstat, the contactor is supplying voltage directly to ground without going through the resistence of the compressor windings and kicking the breaker.
Post back and let me know what you find.