Look when the air should turn on the light of the A/C button if when you release it it goes out and you have to continually press it to keep the A/C on is the A/C on is the problem or control control if it does not come independent, on the condenser fan you would have to use a current tester or test lamp as you call it to see that it arrives positive and negative if it is so it does not serve the engine or you can try it. With two cables it doesn't matter how you connect it if this bad does not work.
Now generally the fans or fan according to the case they enter directly with the compressor, it must always be, in other models they carry gas pressure sensor and work as the A/C system asks it this I tell you because I do not remember exactly how yours works.
Well the compressor to know if it is bad or it is not easy in any workshop will put a manometro or a recovery machine have two low (blue color) (red) low (red) watches will mark 60 psi, high less than 150 psi know without this tool you would have to be fortunate hehe.
I forgot to tell you low marked 60 70 80 psi If it is bad the compressor is 60 psi up a correct reading would be 25 to 40 psi in low according to the environment (night or day) Any questions ask if a friend of the forum knows the answer I do not doubt