OK Olga, just got back home, so I'll answer your question in detail now.
"Can you drive?" does not mean the same as "Are you a driver?"
"Can you drive?" can be interpreted in 2 ways:
1) "Can you drive a car," or "Can you drive this car?" - in the sense of whether they are actually able to drive a car
2) If you and the other person you are talking to already understand the context for your question. For example: if you and your partner are driving in a car, and you stop at a red traffic light. Then when the lights go green, you tell him "can you drive" (so that he drives the car)
"Are you a driver?" - this can also mean a few things depending on the context.
1) The most common is when you ask someone this, it means, if they are a bus or a taxi driver (but again, depends on the context)
2) "Are you a driver?" can simply mean whether they are a driver of a vehicle, any vehicle, since it's not specific. But it will usually mean a car.
To answer your question, which is, if you just want to ask someone whether they know how to drive, just say:
"Do you know how to drive a car?" / or similarly "Are you able to drive this car?"
"Are you a singer?"
This almost always means "are you a professional singer?"
I hope this helps.