One radiator for coolant and air compressor?

The best way to tell is to connect a set of A/C gauges because this kind of compressor does not have a clutch, instead it has an internal valve that is controlled by the AC control module. To see if the compressor is getting a signal you will need to remove the wiring from the compressor and connect a test light or voltmeter.

Here is a guide that can help and the wiring diagram for the compressor:

https://www.2carpros.com/articles/re-charge-an-air-conditioner-system

Check out the images (below). Let us know if you need anything else.