I cannot for the life of me understand how the voltage in this electrical system works.
The voltage used is in the european system. For the U.S it will be 220V for L1-L2 and 110V L1-N.
What I cannot comprehend is the voltage drop when L1 or L2 is connected to the Neutral wire, cause I've been told that the current won't actually be flowing though the neutral, but it will go from L1 to Neutral then return via L2, but how come the voltage drops to 230 then?
What makes the path different if you just skip the little piece of interconnecting neutral wire and connect L1 & L2 to each other directly?
that's because the phase difference among the lines cancels out the currents flowing through it.
I don't know about the european system, but if it's three-phase, then if you only connect two lines there's no way you have balanced loads.
You should read about wave reflection. These animations help:
Basically, if the load impedance is properly matched with the power source, there should be (virtually) no reflection from the load. However, because no electrical device is built perfectly to specifications, there will always be a very small reflection which will result in a standing wave (bad). The neutral wire eliminates the standing wave.
Now the exception is when you do not have a complex load (no imaginary numbers). When your load is purely real, you will not have any wave reflection. This is why some electronics can skip the neutral wire entirely.
From my understanding they're basically one and the same, however referenced in different contexts. If your load isn't balanced across the three lines, then it is not going to be matching the power source.