Crossing the midwest diagonally, you're rarely going to be able to drive faster than 65 mph (legally). Even slow US trains can do 80 mph (though they do stop, too, and frequently get delayed by freight). If you could run trains at even 100mph, which is far from a "modern high speed train", driving would never be faster.
That's crossing the west, or even the west of the west. Trains are slower through that section.
A 100mph train (again, not a modern high speed train) with limited stops would beat the car. Not sure the track could be built for this in this geography, however.
Yes, though the speed limit along the same stretch across Nevada is 80 mph, with the general flow of traffic between 85-90mph. Legality aside, the roads are very high quality and you can cruise along at 100 mph without much difficulty in a car.
100+ mph roads aren't unheard of (see autobahn). Neither are 100+ mph trains. The fact that neither is available is frustrating.