How does an outflow valve work mechanically?
The driving force for the valve is a vacuum source that is connected at the vacuum connection at the bottom of the diagram.  The valve operates by varying suction to chamber 3, creating a pressure differential between 3 and 1 (cabin pressure) that allows the pressure in 1 to drive the valve open (to the left in the diagram) against the return spring.  Take away the vacuum, and the spring will close the valve (move to the right).
The vacuum source is usually an ejector pump in the engine bleed air plumbing, so the vacuum is available whenever the bleed system is on.
So in other words, the valve is sucked open (by bleed-powered vacuum), and sprung closed, and is modulated by varying the suction (by the electropneumatic control valve) against the constant spring pressure.  More suction moves in more open, and less suction moves more closed, and if the suction is completely removed the spring fully closes the valve.
On transport aircraft there are normally two outflow valves for redundancy, but both will usually be located next to each other, typically at the rear pressure bulkhead, and all of the air in the pressure hull will exit at that spot, all of the pressurized zones being interconnected.  Where separated spaces are vented to each other in the pressure hull, but would have a hard time equalizing quickly in a rapid decompression event, like a cockpit bulkhead with the door closed, there will be special blowout panels (like in the cockpit door or elsewhere on the bulkhead) to allow equalization to occur rapidly.
You will also typically find a separate dump valve that opens on on the ground to keep the aircraft from being (slightly) pressurized by ground cart inflow when the bleeds are off and the outflow valves are closed (which can cause problems with opening plug doors), and also to provide an exhaust path for avionics cooling during ground operation with the main doors closed.
The opening size of the pressurization outflow valve has to be large enough to allow more air out than the maximum bleed flow in, so it has to have a fairly large exhaust opening to be able to control pressure at the margins with the pressure hull as airtight as it can be.
Aside from altitude, how much the valve opens in normal flight depends on the main air conditioning bleed inflow (which is usually constant, being regulated bleed flow) and how leaky the hull is (an older airplane with worn door seals, leaky rivets etc, can be quite leaky, and the valve may run pretty much almost fully closed some of the time because of all the air that is getting out through other points - if you've ever been at the forward galley area and wanted to hold your ears due to some crazy howling sound, that's a door leak, and the outflow valve will be running more closed than normal to compensate).