Q1: When one removes a car battery, why does one start with the minus wire? Is it because if we remove the plus wire first it may touch the body of the car and close the circuit, causing a short-circuit that leads to ... what?
Q2: Why doesn't one get electrocuted when touching the minus wire while removing the battery? I'd image that when touching it we'd be part of the circuit and the current should flow through us. What am I missing here?
When disconnecting a clamp from a car battery, there is a danger of creating a short circuit with the tools that are in contact with the battery terminal. So a tool in contact with the positive terminal can cause a short circuit if it touches any piece of grounded metal. Starting with the negative terminal removes this danger; now you only need to ensure it does not touch the positive terminal.
Once the negative terminal is disconnected, the only way to complete a circuit to the battery is to contact the negative post itself. Nothing else in the entire vehicle would complete the circuit if touched by the tools. So it's now safe to be in contact with the positive terminal and all it is connected to.
Electrocution won't happen in any circumstance because the voltage is 12 volts. Even though the battery is capable of supplying many amps, Ohm's law tells us that 12 volts isn't enough to push much current through a person's body.
When you remove the ground cable (-ve in most cars), you are probably touching the body of the car - but the ground terminal is connected to the body, so you don't complete a circuit, and so can't either cause a short or get a shock (though as gbarry's answer points out, you'd barely feel the shock anyway, as the voltage is too low).
When you then go to remove the other terminal, you still can't complete a circuit as you've disconnected the ground, so there is no way for current to get back to the battery.
Whatever you do, don't let any metal tools touch both terminals, or the +ve terminal and the car bodywork when both are connected - the resultant short can cause enough current to flow to weld the tools to the terminals! Similarly, be very careful around the terminals when wearing any metal jewellery (such as wedding rings).
