1. Why doesn't neutral wire give you a jolt? Consider an outlet with disconnected wires and you touch neutral, my reasoning: you should get shocked since for 1/2 of an AC cycle current flows from the transformer toward you -> through you -> into earth, the other 1/2 of a cycle current retreats with no harm since you can't source current from nearby environment?
As you note in your intro, neutral is shorted to earth. Unless there's a large earth potential between you and the grounding rod, you will be at the same voltage as earth, and thus the same voltage as neutral. The voltage between you and the neutral wire will always be very small.
2. Does a coil+magnetic field on secondary transformer winding need a circuit for current to flow or can current flow straight into earth? I learned some time ago that with batteries circuit is needed for chemical reactions to keep on going to create current. If this was true, would for 1/2 of a cycle the current from transformers go through load -> neutral -> earth? Into earth since neutral is bond to earth and not back into the transformer's changing-magnetic-field?
I'm not sure how low impedance the ground is or how easy it is to get a low impedance connection there, but in theory if the impedance is low enough it should work. The return current would flow through the ground, probably back to where your ground rod is to return to the transformer. I believe some transmissions lines intentionally exploit the earth as a return path to save a conductor. There's always a circuit though, the current must return by
some path.
3. Related to the above, wouldn't current on the other 1/2 of cycle go from transformer straight to earth and dissipate all energy because neutral is bonded to earth and not even reach the load/device?
It's AC, so the current alternates direction, (and its voltage alternates +/- about the neutral) but unless there are diodes or other nonlinear components, the path doesn't change. In both cases the return current would flow from the transformer, through the load, through earth, and back to the transformer.
4. After some reasoning, I came to conclusion that since neutral and earth are bound, at any instant they posses same potential therefore there is no difference and no current flows though you? But wouldn't that energize objects that are connected to ground? And wouldn't earth drop some voltage, leading to voltage difference, and possibly zapping you? Wait...what happens when you have a transformer and only connect center tap connected to earth? Maybe that might clear up my issues.
Earth or ground is used as a reference against which the rest of the system pushes. It takes a huge amount of current to induce an appreciable voltage across the ground, the distributed resistance is very low. Sinking the ground rod essentially anchors this neutral point to the same potential as the earth, and anything else in good contact with it, like you. If a voltage (versus ground) ever developed on the neutral wire, it would cause a current to flow into the earth via the ground rod, which can sink a (for practical purposes) unlimited amount of current. A very large current in a single neutral wire back to the ground rod may allow enough voltage to develop to be dangerous, but this would probably also cause fire-hazard levels of heating in the neutral wire, and your breakers would trip long before.
Also was wondering why grounding is encouraged as in safety, I read about examples talking about how grounded device posses low impedance path so in case of a short it can trip breaker easily, others so a microphones doesn't blow up in your face, but I still don't get full picture. Does anybody have good explanation?
The ground wire of appliances is attached to their case, if done properly, by a solid connection that should come disconnected last in a failure condition as well. The idea is that the ground wire never carries current in normal operation, so should always be at a safe potential. In a failure mode where say the hot gets shorted to the case, normally the case would become energized. However, the low impedance path directly to ground shorts hot directly to ground, causing a large current to flow that will trip the breaker, cutting off the power and preventing the case of the device from becoming energized. Having that low impedance path directly to ground ensures that something fails (a fuse, breaker, wire...) if the case ever gets energized, instead of sitting there waiting for someone to touch it and get a shock.
Neutral could theoretically be used this way as well, but would not be safe. Many plugs are wired with hot/neutral reversed, which would energize such an appliance even when no fault occurs!