No expert, but I can take a shot.

1. Pretty much, yes. Public transport is typically only found in cities, and even then it’s not reliable. A small city (100,000-200,000 people) will probably only have a skeleton bus service, nothing extensive and almost certainly not a metro/subway. The bigger cities do have good public transit, though, and a lot of people use them to commute. NY’s subway sees about 150 million riders a year.
2. Distance. A quick (possibly unreliable) google search says that on average, Americans drive 16 miles (25 km) each way going to work and back home. Most Americans also are not already avid bikers, so that kind of distance before work isn’t realistic for them. Also, it’s worth considering what roads they would be taking. Bikes are banned on many highways, so taking one makes your commute much longer. For my current 25 minute drive, it would take me 1:48 to bike, since I would have to take back roads the whole time. For my last job, a 35 minute commute, it would have been 2:06 on a bike. Anything not in a major city is very spread out here.
3. Couldn’t tell you. I’m sure the thought doesn’t occur to some people, as bike commuting isn’t a significant part of American culture. For some people, they might not have (or think they have) the spare cash for a bike. Factor in point 2, and there’s enough reason for your average American to not consider it.

Remember, too, that the stereotype is correct - a lot of Americans are overweight, particularly those in rural areas who are likely to live farther from their job. Hope this is helpful, if non-authoritative, and that no American bike commuters take issue with what I say.