The website says parking at Ibis Budget Sydney Airport is $35 Australian per day. I would not think they have car washing service, a very budget hotel, but does the job if catching an early flight.
Sorry didn't have a car when there. However I know if you phone the hotel they will let you know. Im pretty sure there was car washing close to hotel.
I think the car park is around $20 - $25 a day to park. There is no car washing service at the hotel, there always seems to be doing construction work around the hotel/airport precinct.