right?

"Are you driving?" ~ "Do you have a car?". right?

"Are you driving?" is usually the question asked before two or more people get into a car.

example:

JOHN: "Are you driving?"
MARY: "I don't care. You can drive if you want."
JOHN: "Okay."

"Do you drive?" might in some contexts mean the same as "Do you have a car?" but "Are you driving?" would usually be met with "What, right now?"

Suppose someone had got done for drink driving and you didn't know whether they'd got their licence back yet or whether they were just driving without one anyway, you might then ask "Are you driving?" not meaning actually driving at that very moment.