Yes. They have a demo instance on their homepage with shows and movies you can test it out with

Yes, there are a few relevant features:

1. Playlist: Exactly what you think. You can create a playlist of specific episodes/films/songs in whatever order you want. And yes, you can just shuffle that playlist if you want.
2. Collection: Similar to a playlist, but more loosely structured and dynamic instead of a set list. Just an easier way to logically group together like items to make them easier to find. While this is not a hard-set list like a playlist, you can still shuffle it.
3. Plug-ins like ErsatzTV: Allows you to set up a television-like scheduling system for a playlist/collection. Instead of how you normally use a Jellyfin playlist by simply choosing what you want to watch on-demand, with ErsatzTV, your playlist is constantly playing in the background and you just "tune into" whatever is scheduled to be playing at the moment. Like the olden days of watching broadcast/cable/satellite television. But YOU are the one who created that programming schedule.

You may want to look into software such as ersatztv or disquetv