The fan does that at start-up so it sounds like its working OK.
I have same question about clutch energizing when you jumped it.
It won't hurt compressor if you run it for a few seconds to verify clutch operation.
If clutch does energizes and compressor sounds OK its time to put gauge on system to checkout out the low/high sides.
Also are you sure you had good contact on A/C plug when you checked it for 12V and that the meter was working properly? More then once I have had meter in wrong mode(senior moment) or bad leads.