Cooling is deployed in case the reactor starts to overheat, and that typically happens when water is not supplied fast enough to be converted into steam (or steam output gets stuck). Cooling is not mandatory if you are not using automatic power regulation. However, it is highly recommended to have it as it provides extra protection and helps to avoid any potential overheating.
Bacterial disease spread through contaminated water. To prevent this disease in the future, make sure your settlement has stable supply of clean water.