The water pump is essentially like a simple water pump like on any fountain. The pump pushes coolant from the radiator to the engine and back to the radiator. This coolant flow cools down the motor when it gets over optimal operating temperature.
When the water pump fails or gets a coolant leak it is time to replace. If the water pump completely fails or the leak gets larger you risk overheating the engine and causing costly damage. If there is a timing belt in close proximity it is also a good time to replace if it is showing any signs of fatigue.
There are essentially two types of water pumps; external and internal near the timing belt. An external water pump is significantly less time consuming and easier to replace whereas an internal water pump is near the timing belt and very time consuming to replace. When replacing the water pump, it is recommended to change the coolant, the thermostat and any belts affected by the pump
Any time it shows signs of failure such as a coolant leak or a grinding noise. Water pumps are important to keeping your engine from overheating.
Replacing a water pump requires a certain skill level to do properly. It is messy and easy to make a mistake particularly if a timing belt is involved
Yes, but you run the risk of damaging the engine if it fails to cool the motor. You should not take the risk as the expenses to the damage caused by a struggling water pump can be significant.