The docs are pretty bad, I think they’re working on a much needed revamp of the whole extension section.
As for which page is which, if you go to your developer dashboard and go to your extension, then under versions manage the version you’re currently working on. This’ll be where you configure a lot of your extension settings. When you load the dev rig, it uses the provided extension client id and version to pull all these settings from Twitch, so it knows which HTML file is which, and all the other settings. This version management page is also where you’re do all the stuff like uploading assets to Twitch for hosted testing, setting test channels for when you test on a live channel (and also for when you get to the review stage, as reviewing has to be done on a live channel).
As for the EBS. Twitch have nothing to do with that. If your extension needs to contact it, then in the javascript you can use fetch which is a built in API for handling HTTP requests (google it if you need documentation for how to use it, there’s a huge amount of guides and docs), and there’s numerous alternatives too. You just need to make sure it’s over HTTPS, and that your EBS is both publicly accessible to the internet (so not behind a firewall that’d be blocking it) and you’ve created routes on whatever webserver software you’re using to listen for the incoming request and handle it.
If you look at the viewer.js of the Hello-World example extension you can see how they perform a HTTP request to the EBS using jquery’s ajax, so if you want to go the jquery route then that’s an option. In their backend services file you can also see an example of using Hapi for a webserver, and how they’ve set up routes for different API calls to the EBS.