Hayase is bring-your-own-content and does not offer anything, however gh:hayase-app/extensions is recommended.
No. Hayase is not directly associated with any extensions or sources. It's merely a client for streaming one's own media.
Inside Settings > Extensions > Repositories you can add extension repositories by either inputting a full URL such as https://example.website/manifest.json or if an extension is published on npm packagename and pressing add, if its hosted on GitHub you can use this prefix: gh:username/repo. This will automatically import all sources the extension provides. You can then uninstall an extension by going into the extension options and pressing the Delete Extension button.
You can disable sources in the sources list by clicking on it's toggle.
Extensions for Hayase need to be written in JavaScript which are run in an isolated Web Worker. Make sure the data you're fetching is CORS enabled. Extension type definitions and an example implementation are available on GitHub.