Tapping it won't hurt (assuming you control yourself). The weird readings with the system off suggest there could be an obstruction somewhere. Any chance someone put in one of those leak-stop products? They can really gum up a system like this.

Some of those readings are low enough the low-pressure safety switch may be keeping the compressor from running. I will try to look up that pressure value for you when I am home later.

Have you confirmed the compressor clutch it is clicking on and off? The belt spins the pulley all the time, there is an electrically actuated clutch that has to be engaged to actually turn the compressor. You should be able to hear that click on and off as the compressor cycles if you are in front of the car.

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David.X5
2001 X5 4.4i Sport
SOLD! at 160k miles