1) Yes, there is a motor inside the compressor.
2) Yes, the relay inside the little black box is called a start relay, and it's either solid state (PTC) device, or it's mechanical. If it's solid state, just get another one as it's not easily tested. If it was mechanical, you should be able to see a heavy coil of copper or aluminum wire wrapped the outside of it. The rattle is a plunger/switch which makes up part of an electromagnet created by the coil.
If the relay doesn't rattle, then the plunger is welded in the closed position, and that will cause the compressor to run about 30 seconds, then trip out on internal overload. When the overload cools, the compressor tries again, and the sequence starts all over again.
And, so far, you've described nothing but an electrical problem. Don't go fishing into the freon side of the system because your looking down the wrong road if you go there. Unit's like this don't usually have low suction pressure switches on them (which would cause actions as you describe.). But, this unit's sounds too new for that to be the problem.


1) Yes, there is a motor inside the compressor.
2) Yes, the relay inside the little black box is called a start relay, and it's either solid state (PTC) device, or it's mechanical. If it's solid state, just get another one as it's not easily tested. If it was mechanical, you should be able to see a heavy coil of copper or aluminum wire wrapped the outside of it. The rattle is a plunger/switch which makes up part of an electromagnet created by the coil.
If the relay doesn't rattle, then the plunger is welded in the closed position, and that will cause the compressor to run about 30 seconds, then trip out on internal overload. When the overload cools, the compressor tries again, and the sequence starts all over again.
And, so far, you've described nothing but an electrical problem. Don't go fishing into the freon side of the system because your looking down the wrong road if you go there. Unit's like this don't usually have low suction pressure switches on them (which would cause actions as you describe.). But, this unit's sounds too new for that to be the problem.

Yes, the motor in the compressor will run.

There are two windings in the motor, inside of the compressor. A start winding, and a run winding. Both windings are energized when the thermostat says "Make it cold in here.". But the start winding should only stay powered, through the start relay, for just a second or two, until the motor begins to run. Then the start relay drops the start winding out of the circuit.
If the start relay does not drop the start winding out, the motor windings heat up, causing the internal high temperature reset to trip out (possibly after 30 seconds that you indicated.). Once it cools, the whole process starts over again.


Yes, the motor in the compressor will run.

There are two windings in the motor, inside of the compressor. A start winding, and a run winding. Both windings are energized when the thermostat says "Make it cold in here.". But the start winding should only stay powered, through the start relay, for just a second or two, until the motor begins to run. Then the start relay drops the start winding out of the circuit.
If the start relay does not drop the start winding out, the motor windings heat up, causing the internal high temperature reset to trip out (possibly after 30 seconds that you indicated.). Once it cools, the whole process starts over again.