(b) Gate agents book a flight out when it leaves the gate. They don't hang around to see whether it actually takes off. IMO this needs to change. Gate agents should be "responsible" for the flight until it physically departs, even if they are handling subsequent departures. Otherwise you get the scenario (as happened to a friend of mine recently) when the last flight of the day is delayed taking off, and eventually returns to the gate and is canceled because of a mechanical. Long before then, the gate agents have packed up and gone home, and there is no one left at the airport to service the passengers' overnight needs and get their luggage back, let alone rebook them the following day.
This makes no sense, there are far more productive uses of GA time.