Yes, admission to the Villa is free, but they charge for parking, and require a reservation.
Shuttle... was a donation to get into the Science Center, and I think you could get a guaranteed spot in line for $2, but if you wanted to wait until there was space available, that was included with your admission. I didn't pay anything other than the entrance donation to see her. The Science Center/USC Rose Garden/Natural History Museum are on a light rail stop, on the Expo line, if you don't want to pay for parking. Worked beautifully.