So yes, there is unemployment insurance in the US, and it pays almost 30% more than in Sweden. There is a HUGE gotcha, though, and that's the cost of health insurance. Unless the former employer is subsidizing, that costs about $400-700/month. There are, in general, far fewer social welfare services to rely on as well.
That said, like you, I wonder if this is an American thing. It feels to me as if many Americans are one job away from total collapse, like their country is only ok for people with a good employment and an utter nightmare for everyone else, with no safety net at all except your own savings. With that in mind, a year without a job prospect would indeed seem like living in hell.
Yes, that is pretty much correct. Many many Americans, even ones considered well-off, live a threadbare existence. To Europeans it's unfathomable what can happen in the United States but it's just as bad as you think if not worse. There is literally no bottom in this society, there's no limits to the depths you can fall.