First, NEVER work anything hot. There is no such thing as a safe voltage to work energized. Even a simple home receptacle circuit can easily kill you (and it happens with alarming regularity).
That said, ALWAYS work something AS IF it were hot (for the exact reason you said, accidents happen). This means connecting the safety measures first. The safest order to connect wires is: ground, neutral, hot. The safest order to disconnect wires is the opposite: hot, neutral, ground.
Half right, half wrong. It would not short if it touched the metal box, and would not trip the breaker. That part is right.
However if it touched YOU not having the ground wire connected actually helps you. It means the electricity does not have as a good of a path back to the box, and you'll get a weaker shock.
With the ground wire you'll get a much higher shock, but it won't trip the breaker!! Humans have too high resistance to trip breakers, you'll just keep getting shocked.
So it's kind of a wash - with the ground, it's more likely to just short against the box and trip.
Best is just to always wire things as if they are live. Only touch the wire if you have to, always use insulated tools, even if the power is off.