Livestreamer is a command-line program that opens streams with a native video player like VLC.

Streamlink is a fork of livestreamer, since livestreamer is no longer maintained.

Go to the extension settings and set the stream URL copy pattern to the streamlink command you want to run to open a stream. This would for example look like streamlink {URL} source.

You can then copy that command for a channel from the context menu in the panel and then execute it in a console to launch Streamlink.

No, but an integration with the Streamlink Helper Extension is in development.