Why do we not get shocked by neutral wire and how can it behave as it does?
The neutral wire is tied to a potential of 0V in comparison to ground with a very low resistance. This means, that high currents can flow through the neutral wire without any noticable voltage appearing on the neutral wire (Ohms law: U = R*I). Without any voltage on the neutral wire you can not get shocked (the high current can only flow through the neutral wire because of its low resistance. Your body has a pretty high resistance and needs some significant voltage to get a current flowing).
Your first picture is the correct way to connect the light bulb. The live wire supplies the high voltage (110V or 230V) and current, the neutral wire is sinking the current. In your second picture both terminals of the light bulb are connected to the same potential - both to the live voltage. Without a potential difference between the terminals, there will be no flow of current through the light bulb (again: U = R*I or I = U/R). At the same time you are connecting the live wire with neutral wire without a load in between - this will create a short circuit and a very high current. Hopefully the circuit breaker would trigger in this case ;)
As I wrote above, the neutral wire has a potential of 0V and sinks the current back to the generator (or actually to the next transformer). It does not mattter whether the live voltage is positive oder negative. You are right, the polarity is changing rapidly with either 50Hz or 60Hz (depending on where you live). The only thing that changes is the direction of the current flow. In the case of a positive live voltage you have a positive current and in the case of a negative live voltage you have a negative current (minus sign just means, that the current flows in the other direction).


Edit: See the picture below. The neutral wire is on 0V, which is represented by the black horizontal line in the middle. The live voltage follows the curve of a sine wave and is alternatingly positive and negative. When on positive potential, the potential is higher than neutral, but when the potential is negative, it is actually lower than 0V. The current is always flowing from the high potential to the negative one, so when the polarity of the live wire switches, so does the direction of current flow.


Image from learn.sparkfun.com