It's not an AMP thing per se, it's how Google handles AMP in search results.
No, its explicitly an AMP thing. Google serves the user a cached version of your page directly from its servers, hence the google.com/amp/ url
No, it's not. See Nuzzel's implementation of AMP, it opens the AMP version on the host.
I run a WordPress blog. From the documentations of Google and WordPress AMP plugins, I have always thought that the user will be directed to "originalurl/amp" on my domain when they click on the Google link on their phone. Now that I see it's a Google domain, this is really weird.