I've read many of the proposed questions in this thread - does the CEO have daughters, does the company send everyone to conferences. I personally would avoid asking "what's in it for me" questions unless the company has shown strong interest.

I remember one candidate who received an offer, then insisted on meeting with the CEO a second time and asking him a few more questions. She never got that meeting; the offer was rescinded. The CEO saw her demand as a bad sign.

Any weird question you ask during this sensitive phase will get analyzed and raise concerns. In other words, you have to gather your info via other means.