Are there other coolants besides water?
Water would be it, essentially. The reserve tanks at a reactor contain the same grade of water in terms of purity and chemical composition that are normally used in the core. It is possible, if you have a situation where you have exhausted that source of coolant to introduce, quote–unquote, regular water. That will do the job of cooling.
Why do nuclear power plants need electricity to be cooled?
Nuclear reactors are net positive in terms of supporting the grid. They produce much more electricity than they need to run their systems. As a basic design feature in the U.S., plants are not literally self-powering. That's by design, because you don't want to end up in a situation where a problem at the plant cuts off its own power source. Therefore, the primary means of power for a plant in order for it to run is electricity from the grid. As a general matter, for U.S. plants, if you can't use power from the grid, you shut down.
What kinds of events could knock out a diesel generator?
You always have the possibility of just plain old failure. That's why you have multiple diesels at a plant for redundancy's sake. It can be the case that diesel itself is running properly but the distribution system, the buses or the cabling could be misaligned to the point where the diesel detects that its power is not being accepted by the plant. It's not going to run if it's trying to generate power and that power's not going anywhere. When we say a diesel fails, it's not always a problem with the diesel [itself].
How long does it take to cool down a reactor?
There are design specific variables there. The easiest way to answer that question is that NRC regulatory requirements for emergency power supplies is that they be available on the order of a month. You can render a plant in an acceptable condition within a few hours. However, heat is still being generated. If you had to stop, at any point, carrying away that heat, it would start building up again. Emergency cooling systems have to be available for weeks.