It's possible that there is also a script that alters the markup after the page loads.
No, that's extracted from the DOM using Firefox's DOM inspector.
It could be manipulated onhover
It doesn't take up space. You can't hover over it.
I've seen this sort of thing for fraud detection before. Given that they make money off of clicks, that seems important.
Most likely.
It is sometimes also used with forms as an easy way to detect bots: an extra input with a display:none is used to filter out bots submissions.