I've been to the US a couple of times and most restaurants I visited did not have any parking spots at all. I have also seen plenty of food-carts operated by a single person, comparable to the Japanese mini-restaurants described here.
I'm guessing you stayed in a major city and didn't drive anywhere outside of it? If you flew in and didn't have a rental car, odds are your itinerary was biased towards places that didn't need a car?
Yea, the vast majority of restaurants in the US do, but the US is insanely huge and the places tourists are more apt to visit are higher density.
It's not federal. It'll come down to the state and municipality. If you were in a denser city, it's likely they didn't have that requirement. Lots of New York City doesn't have this kind of requirement, but you may see that if you were in a more suburban area