Q:“How can I see what playlists a channel has?”
Well, if you're the admin for a channel, you can look in the Content section of the admin area, under playlists, and click view. That will bring up a list of all your admin or user created playlists.
If you're a channel user, look at the channel navigation bar, and click Playlists. That will take you to a page listing all the channel playlists, including the built in ones.