Dominique, I will not answer all of the questions in your post, except to say that collective ownership of roads is not the function of the government. The purpose of this post is to ease your mind on the economics of private transportation.
First off, the goal of private roadway companies would be to ensure as many customers and income as possible. To achieve this they would need to keep tolls low, keep roads safe, ease congestion, and keep payment simplified.
In the case of toll highways, there are already electronic passes that bill your credit card when you pass under a radio frequency identifier. You purchase the cheap and simple RFID from the company, put money in an account with them, and you are able to drive on and off of toll highways with no congestion and lines. Any company to implement this type of service on the free market would earn more customers.
On streets in commercial areas, the businesses in the district will probably pay to maintain the roads themselves, and will not place any charges to drive through them. Their incentive is to get customers to their stores, not to drive them away.
In residential neighbourhoods, roads will generally be built by developers and landowners. In my case, I live on a privately built and maintained road sustained by the strata fees required by people living in the condos. It snowed today, and a backhoe was hired to clear the snow early in the morning.
It is in a road company’s interest to connect drivers smoothly with other roads, even if they are going to a competitors roadway–otherwise he would have no customers. To expand his market, he wants to connect to as many other roads as possible, and make his roads inviting to drivers.
Eliminating the enormous subsidy for automobile orientated transportation and delimiting regulation on other forms of transport will spur fast, cheap, and convenient methods of travel. If the market is there, a bullet-train will be built by a company looking for a profit (like Dagny did). When rail-transit systems are built, there is little need to worry about compatability with other companies because they are point-to-point transportation.
What I find enormously backward are the regulations on vans and cabs in North America. Go to Asia, and a man with a van (or even motorcycle taxi) can make a living driving people to and fro. You often pay only half a buck to drive half way through the city. I’ve heard that business liscences for cab drivers in New York are thousands of dollars now. I’m sure the same is with buses, otherwise we would see more private bussing like in other countries, rather than almost purely government subsidized public transit.
[Edit]
[This bridge is completely privately made]
[Who Cooked the Jam? An article on roadways by the Von Mises Institute]