Do the panelists — or the listeners — know what they e going to be asked in advance?
No. During the week, the crack Wait Wait staff at HQ in Chicago researches and writes questions, based on their news value, potential for humorous wisecracks, and funny accents for Carl. Neither the panelists nor the listeners know what they will be asked, although, being sensible people, they know that if Britney Spears or Arnold Schwarzenegger does anything even mildly odd during the week, it will probably come up.