Is "mustn't " used in everyday speech ?"Forbid" is a rather forceful verb, as SwissPete says. If you were to use it, then "I forbid you" is the usual expression.
"I'm forbidding you" is rare, and would only be used after some time discussing or arguing about the matter. Perhaps if the other person had failed to grasp your opposition to their using your car, you might say something like "Look, I'm forbidding you to use my car, right!". I am not sure whether the continuous form is used for emphasis, or because by the time you come to use it, the discussion has been going on for some time so might be regarded as a continuous action, but either way this usage is unusual.
"You mustn't use my car" has a similar meaning to "I forbid you to use my car", but is used in a wider range of circumstances. You might say "You mustn't" when the other person had made no suggestion of doing the thing, but "I forbid" is always in response to a threatened action.