Unless I've misunderstood the details, it might be a good idea to look at question 5 first because if there is indeed voltage at the wiring for the compressor when the ignition and/or ac switch is off then you have some very serious mis-wiring issues to attend to before anything else. There should be no power at all at the green leads (and subsequently the compressor) unless both the ignition and the ac switches are on. Otherwise the compressor clutch would be engaged permanently, which would probably draw enough current to flatten the battery overnight.
Other than that:
Qu 1: The pressure sensor is screwed into the accumulator (which might also be known as the reciever/drier) and has a single plug with two wires attached to it. My guess (and it is only a guess) is that it is a 'binary' switch. That is, it cuts power to the compressor if the refrigerant pressure is either too low or too high. Testing the switch normally requires a pressure gauge to be attached to the ac system. The switch is normally pretty reliable though.
Qu 2: The belt driven pulley rotates all the time while the engine is running. The compressor is engaged by an electro-mechanical clutch which is activated by the wire to it which comes from the pressure switch. The disc in the centre of the pulley is the part of the clutch which is attached to the compressor and is engaged with the pulley when the clutch is activated. As previously stated, if the compressor isn't siezed, the central disc should be able to be turned by hand while the engine is switched off. Don't put your hands near it with the engine running. If it is hard to turn then chances are the compressor is dead, or the clutch is out of adjustment so that it is dragging when not engaged.
Qu 3a: Battery leads - Positive to the single wire to the compressor, negative to the compressor body.
3b: When an electrical connection to the clutch is made, there should be an audible click, and the central disc of the pulley/clutch unit should rapidly move toward the compressor a small distance.
3c: It can be tested with the ignition and ac switched on. Better to do it that way than with the engine running, so that the operation of the clutch is more audible and visible.
Qu4: If there is only one wire at the compressor then the negative electrode of the voltmeter should be placed on the compressor body, which is earthed to the battery through the engine. If there is another wire from the compressor which is grounded, then use that.

There are a lot of apsects of an ac system which can give trouble. If your knowledge and experience with ac systems is limited then tracing and rectifying the problem(s) might best be left to a specialist to carry out. Chances are the system will need evacuating and re-charging properly regardless of the fault, which is definitely a job for an aircon shop unless you have the proper (expensive) equipment and a sound knowledge of the procedures.