Sort of. It doesn't have to be a traditional file or anything, so it helps to think of it as a unique URL being accessed instead of a different pixel. What makes it work is the client automatically loading all images, which means the user accesses the URL automatically as well. It stops working if the client uses features that disable automatic image loading.

You could implement this by sending each email with an img tag that has a unique url, such as https://foo.bar/baz/id_1.jpg, which the server will route under the hood to a script. The script stores the fact that someone visited id_1, assumes it must have been the recipient since only they have the URL to get to it, and responds with image data to make the whole thing seamless.

Yep. Each user gets an email unique to them.