My car's RPM meter says x1,000 for each notch, therefore when set to 2 this implies 2,000 RPM. I can't visualise an engine's flywheel turning 33 times per second when the car is set to 2,000 RPM - it seems excessive. Have I misunderstood RPM or is that actually how fast the heavy flywheel turns and the pistons rotate the camshaft?
yes, that's correct. Now, rotating a flywheel at 2000 rpm is not a big deal: it's well within the capabilities of the material, as long as the flywheel is well-balanced. Other elements in the engine undergo much higher loads.
The pistons, for instance, also go through a full stroke (up+down) 33 times per second at that engine speed, going from 0 to 100 km/h on each stroke. Pistons experience G-forces in the region of 1000 G. Valves undergo similar forces.
These forces are one of the limiting factors in engine speed: these accelerations are so high, you come up against the tensile strength limits of the materials used. High-performance engines require special materials and construction techniques for the pistons, conrods, crankshaft and other reciprocating items.
RPM stands for ROTATIONS PER MINUTE. Converting to RPS (rotations per second) means you divide RPM by 60 (because there are 60 seconds in a minute) and you get RPS.
So your question on 2000 RPM gives us: 2000/60 = 33.33333... rotations/second.
Many modern engines go run much faster than 2000 RPM. Formula 1 engines run in excess of 20,000 RPM which is 333.33333... rotations/second.
You have, however, understood this correctly. While this may seem fast, some devices turn much faster. If you have a turbocharger on your engine, that may turn at speeds of 100,000 RPM or more.