If the overload trip contactor has a separate set of contact it is possible to use it to indicate the trip status to a PLC.
Otherwise, attach a relay coil to the power terminal to the compressor. If the compressor is receiving voltage then the relay is energized and the contact closes. If the power has tripped, then the compressor will receive no voltage and the relay will de-energized and its contact open. This form an indication to the PLC whether the compressor has tripped.
You can only get analog reading from a thermostat provide it has an analog output. Most thermostat provide only an on/off signal to to control system and depending on the signal voltage availble you could use the PLC digital or analog input to monitor the on/off status.
