Yes, but there are also a lot of times where they don't in my personal experience. If there's a question about who technically got there first - like two cars approach at roughly the same time - the rules aren't always followed as written by other drivers.

Not in my experience. Of course, as long as people are actually stopping, someone already stopped has an advantage. But that's a difference between East and West Coast US driving. In the East people come to a complete stop before moving again. In the West they'll slow down a lot, nearly stop even. So there's definitely regional characteristics. But the most common law is that of our childhood, possession is 9/10ths of the law.

First to stop is the safer option. I feel that most people around here follow that too.

It also has a rare benefit of seeing the interaction between a majority first-to-goers at a 4 way.