Can people with epilepsy continue driving?

Yes but. ...The rules vary from state to state. Consult your local department of transportation and talk to your doctor. Many require the doctor to report a patient who has had a seizure. If you have had a seizure you should not drive until they are controlled, depending on the laws in you area.
Yes. Assuming they're epilepsy is well controlled and the haven't had a seizure for 6 months. Each state or country is different with their own laws.