Unfortunately, it doesn't always work out that way, because congestion tends to be the limiting factor for demand for car trips thanks to a very low perceived marginal cost. So as soon as congestion reduces somewhat, that extra capacity suddenly makes it more attractive for the marginal driver to take a marginal trip, and traffic increases (but not quite all the way back up to its original level).
Not if more people forego the car entirely. The marginal trip costs are high if you don't have a car. Even if you could rent one cheaply over the weekend, it's more marginal cost than if you have it in your garage.
A lot of European cities with good public transport and narrow medieval roads still have less traffic than American cities with 4 lane roads.
