Apps. Websites or desktop or mobile programs. Communicate using apis.

Apis are like gateways/doorways to data so that one program can get data or post data or put data to another servers application.

The Chrome extension is a standalone application that Chrome injects into the browser and that extension is making calls to YouTube servers asking for the dislike Data using the YouTube api.

Without that api the data cannot be accessed externally.

Definitely possible. Dissenter did something similar by adding an external comment section to every website. Unfortunately these things are not very useful unless a large number of people use them. And in the beginning, nobody has much incentive to use them because the number of users is low. Chicken and egg problem.

In the end, all this really does is quarantine the evil nazis into their own little bubble, hidden from everyone else. And they're perfectly fine with that, as for them the whole point of hiding these things is to hide the truth from people who aren't aware of it yet.

It is possible. There's already a browser addon that automatically skips ads inside videos based on timing submitted by the users of said app. I bet making a dislike tracker with minimal botting protection should be similarly easy.