OK, let me explain some things. There are 2 problems: one related to measuring AC voltage between Hot and Neutral in a ceiling point, and another one the breaker tripping when I soldered the neutral.

1. The one I didn't understand was the DMM reading 20-60V AC between Hot and Neutral with the ceiling switch off. I am learning now that there can be stray voltage and that I should short both wires (load with a light bulb I mean, for example), even after switching off, to drain whatever remnant voltage. I am curious about that and will try it in my own home one of these days. My question here is... is stray voltage really an equivalent of saying that the 2 wires are somehow "charged" with so very little energy @20-60V, and that the DMM is reading that? So if I drain with a bulb the stray voltage, REMOVE the bulb, and check again, I should read almost 0V? Or does the stray voltage come back when there is no load?

2. The other problem is my iron, which tip is grounded, and when I touched the switched off neutral (which now I believe is not affected by the switch and is still connected to the rest of the house circuit), the main breaker tripped. I was not understanding this because if neutral is at 0V, and ground is 0V, there is no current and I don't understand how that could trip anything. Now I am learning that you guys say there can be some voltage in neutral and that can go to ground and trip the breaker.
Is is that the correct answer, or this is not voltage dependent, but simply whenever you short neutral and earth you are going to trip the main breaker, no matter if there is current flowing or not?

 

Even if it not a dead short, even quite a large resistance will divert 30mA away from neutral and trip the RCCB

I was contesting the short from neutral to earth, which I did not mention!

 

OK, let me explain some things. There are 2 problems: one related to measuring AC voltage between Hot and Neutral in a ceiling point, and another one the breaker tripping when I soldered the neutral.

1. The one I didn't understand was the DMM reading 20-60V AC between Hot and Neutral with the ceiling switch off. I am learning now that there can be stray voltage and that I should short both wires (load with a light bulb I mean, for example), even after switching off, to drain whatever remnant voltage. I am curious about that and will try it in my own home one of these days. My question here is... is stray voltage really an equivalent of saying that the 2 wires are somehow "charged" with so very little energy @20-60V, and that the DMM is reading that? So if I drain with a bulb the stray voltage, REMOVE the bulb, and check again, I should read almost 0V? Or does the stray voltage come back when there is no load?

2. The other problem is my iron, which tip is grounded, and when I touched the switched off neutral (which now I believe is not affected by the switch and is still connected to the rest of the house circuit), the main breaker tripped. I was not understanding this because if neutral is at 0V, and ground is 0V, there is no current and I don't understand how that could trip anything. Now I am learning that you guys say there can be some voltage in neutral and that can go to ground and trip the breaker.
Is is that the correct answer, or this is not voltage dependent, but simply whenever you short neutral and earth you are going to trip the main breaker, no matter if there is current flowing or not?

1. Your DMM will have a input resistance of 10MΩ. Therefore it will need just 6uA of current to make it read 60V.
House wiring cable has a capacitance of about 100pF per metre. So about 800mm of cable could have enough capacitance for your meter to read 60V. Capacitance from cables that are still energised could easily amount to the required 80pF.

2. Let's call the point where Neutral and Earth are commoned, where the supply enters the building "0V". If there is current flowing then nowhere else will be 0V. Ohm's law tells us it will be the neutral current x the cable resistance. So there will be a voltage on the neutral wire at the point you touched it with the soldering iron. The neutral current then has a choice of how it gets to the point we've called 0V. It can go through the network of neutral wiring and the RCCB, OR it can go through your soldering iron and the network of earth wiring. If more than 30mA goes through your soldering iron, the RCCB will detect and imbalance of 30mA and will trip.

 

1. The one I didn't understand was the DMM reading 20-60V AC between Hot and Neutral with the ceiling switch off. I am learning now that there can be stray voltage and that I should short both wires (load with a light bulb I mean, for example), even after switching off, to drain whatever remnant voltage. I am curious about that and will try it in my own home one of these days. My question here is... is stray voltage really an equivalent of saying that the 2 wires are somehow "charged" with so very little energy @20-60V, and that the DMM is reading that?

There are 'stray' voltages and signals all around us, especially in heavily built up areas, you can walk across a carpet and induce a charge in your body.
Another example is when you grasp the input lead on a 'scope' you will commonly see a 50/60hz waveform, this is stray fields from the nearby service conductors.

 

Thank you, that was enough to understand better the problems I was having.

Still one question has not been answered. I believe, then, that I could discharge the cables capacitance, just like you would do with a capacitor, by putting a load between the wires. The question is... according to my thinking, since you have discharged the cables, the load must not be connected in order for you to read almost 0V this time, right?
How much time passes after the cables get some energy again to trick the DMM and show values of 10V or more?

Will they get energy even if I keep the switch off for, lets say, 5 years?
That's 5 years the hot wire has been disconnected from everything, and there is just like 4-5m of hot wire cable between the switch and your DMM probe connected to nothing. The neutral though is still connected to all the return circuit.

If I think about it deeply, I ask myself more questions.
Why is the voltage AC? Or is it not?
What's the frequency of that AC voltage? 50Hz? Why? What is pushing and keeping that voltage?
In an electric motor it's the speed of the rotor that must be maintained to meet the 60/50Hz, but here I wouldn't understand how it could be AC with a fixed freq.

I can think about it as a capacitor, and then the voltage should be DC, no freq, no wave.

 

The voltage is AC, and the frequency is 50Hz (didn't you measure it with the AC setting on your meter - and does your meter have a frequency range you could use to confirm it).
You have a capacitor between mains-live and your "disconnected" cable, and a resistor (10M in the meter) between the "disconnected" cable and ground. It's a high-pass filter. The capacitor is the sum of all the capacitances between your disconnected cable and any mains wiring.
The voltage will return the moment that you remove the load. The current will remain the same whether the load resistance is present or not.
There will also be inductive coupling from any devices which produce an alternating magnetic field - motors, transformers etc.

 

Why is the voltage AC? Or is it not?

There have been posts here and elsewhere where someone has built a circuit with galvanic isolation via transformer etc.
They have shown concern when measuring from the DC power common to earth GND and measuring a voltage with their high impedance meter..
After instruction to connect a fairly low value resistor from chassis to GND the voltage disappears.
In many cases such as this, a 10Ω resistor can be permanently connected from the chassis to earth GND.