Ok, let's start from the same picture so we're on the same page:
These engines are four stroke engines, which means the piston goes up and down a total of 4 times, twice up, and twice down for each cycle.
So to answer your questions:
Of course I do realize it stands for revolutions per minute, but revolutions of what?
As you stated later, it's revolutions of the crank shaft.
I assume the crank shaft, how is it calculated, is it by the crank shaft sensor? Why do some old cars that runs with a carburetor don't have the RPM meter is it for the lack of the ECU and the sensor?
As for how it's measured, there are both mechanical and electrical ways to measure it. Older cars didn't have a tachometer just because they were not popular, and to limit the cost. Many older cars did have tachometers though, just mechanically driven. I'm not 100% sure where the pickoff was for this, but if I had to bet it was just a gear off the crankshaft that gets reduced to a needle movement on the dash. In the same way that the speedometer was usually a gear in the transmission that did the same thing just for wheel speed.
As for the electrical methods, yes, it's just a sensor talking to the ECU which sends the right PWM (Pulse Width Modulation) signal to a gauge in the dash.
Also assuming a 1000 cc big 4 stroke engine with 4 cylinders running at 1k RPM how many times are each cylinder firing per second or how can that be calculated, also does the piston "revolve" the crank shaft with each stroke even at the exhaust stroke with the same torque or is it different at the firing stroke, if so how is the RPM not constantly going up and down with each different stroke
To lay this out, lets look at how many times the shaft rotates with each stroke. From the diagram you can see that a full up and down path of the piston makes for one revolution of the crankshaft. That means in a four stroke engine the shaft rotates twice (two revolutions) for every four stroke cycle, which means one power stoke for every two revolutions of the crank. So, if the crank is turning 1000 times per minute, that would be 500 power strokes (firing of the spark plug) on each cylinder in that one minute. Since there are 4 cylinders, there would be 2000 sparks in that one minute across the whole engine.
And no, the piston does not produce the same torque on every stroke. In fact it only produces torque on the power stroke. The other three it's just along for the ride.
As for why RPM does not vary constantly, the plugs don't all fire at once. The power strokes are spread out so that during the rotation of the crank the power is divided amongst the 4 cylinders so one of them is almost always producing power and turning the crank. In addition, the flywheel has a lot of mass, and tends to smooth out the roughness of each individual cylinder firing during it's power stroke. Otherwise it would be a much rougher cycle.
I think that covers it all, if anyone finds something I missed, or if I managed to get something wrong, please yell and I'll just edit it so we have this right.
I hope that helps!