If you (git) checkout the project you can use either `yarn repl` or `yarn live-stream` in the `packages/rrweb` folder to play with it locally

It does. Everything is open source and from what I see there is no official server – you can store captured sessions anywhere you want.

Yeah, it usually comes included on some analytics platforms like Posthog, or UXWizz which can also be self-hosted and ran locally.