Climate in the car

I have three questions about the climate:
Where are the measuring points in the vehicle so that the climate knows when it needs to cool or not?
Does the climate compressor have its own relay ?
Can you read the current interior temperature on the display (have the old one in the vehicle) ?
Additional question: Can one exchange the old display for the new without much effort?
Wait for your answers, as usual, factual and understandable !
Cheers and greetings from Steffen from Thuringia.