Oh yes they do, and why would you want to break network caching to spy on your users? You can always add some little js to ping your server (logs! Again!) or a non-cacheable tracking pixel.
Sure, you can do that. Google Analytics is merely a free version of that service.
Free to you, the user pays with their data. This is apple giving the user the option not to subsidise the website operator.
Tracking (especially first party) is not some shadowy value extraction scheme. You need at least some data to improve your service and understand what brings traffic to your page.
The developer also pays. By giving Google their entire viewer/user base, so Google knows whom to target if they decide to create an alternative.