1..."Can" and "be able to" are very similar and are often interchangeable.
In your 'car' sentences, maybe one say that "can" emphasizes having the knowledge and practical training/experience needed to drive a car, while "is able to" emphasizes the present ability and availability to drive a car.
He can drive a car, but is not able to do so now because he has a broken ankle.
I don't want to overstate this 'difference' and I am not sure how many other people would make this distinction. Maybe someone else will offer an opinion.
2...I don't agree. Passive voice can be used with perfect progressive tenses. I have been receiving phone calls from him all day.
I don't think that "The car has been being washed for 2 hours" is a good sentence at all! 'The car has been getting a wash for 2 hours.' is fine.