Walk past a closed bathroom stall fast enough and you can essentially do that with your own eyes. Or stand there and quickly shift your head side to side. Just don't do it on one that's occupied, that's not cool.
Only in the US. The rest of the world has doors without a gap at the sides.
You clearly haven't traveled much so you should refrain from sweeping generalisations.
Not every bathroom stall in the US has gaps either.
Mine was that, typically, people from outside the US, only ever experience toilet stalls with gaps when they visit the US.
Not every stall has gaps there, but I don't recall ever encountering it here in the EU.