What are the risks of a brain CT scan?

Very safe in general. A plain ct scan really only caries the risk of a fairly modest radiation exposure, so we typically only start to worry about this for people who get many cts in a single year. If it is being done with intravenous contrast, then there is a risk of allergic reaction to the iodine, as well as some risk of kidney damage in those with underlying kidney risk factors (eg elderly, diabetes).
Extremely low. The risk of a brain ct is extremely low. Radiation is utilized, however the dose you will receive is not enough to cause injury.