Likewise, are neutral and ground the same thing?
Under normal conditions, a grounding conductor does not carry current. Neutral is a circuit conductor that normally completes the circuit back to the source. Neutral is usually connected to ground (earth) at the main electrical panel, street drop, or meter, and also at the final step-down transformer of the supply.
Subsequently, question is, why do you tie the neutral and ground together? “Whenever you have an auxiliary panel the neutral and ground should not be tied together because the ground wire becomes a parallel path for current with the neutral wire (any current going through the neutral wire will be shared with the ground wire because they have the same connections at both ends).”
Keeping this in consideration, is it OK to connect neutral to ground?
No, the neutral and ground should never be wired together. This is wrong, and potentially dangerous. When you plug in something in the outlet, the neutral will be live, as it closes the circuit. If the ground is wired to the neutral, the ground of the applicance will also be live.
Can you touch the neutral bus bar?
If the main breaker were on, all of the exposed stabs for the bus bar are all going to be carrying electricity. So you're not going to want to touch any of that. The neutral is also a potential shock point if the power is on. Try to avoid touching any of the incoming service lines.