NG--It seems like there isn't an OA person around to answer any of your questions.
Try OmanForums and you will find a wealth of information on life in Muscat. They will have information on schools etc as well. Not sure what the schooling allowance is at Oman Air, but the schools will run around 3,000 Riyals approximately per year depending on the age of the child and the grade attending. The British School seems to be highly regarded but there is a long wait list. For housing try Oman Homes on the web. I think you will be able to find a villa for around 1,000-1200 Riyals a month (4 bedroom). An area called MSQ is listed as an expat neighborhood. Not sure of the distance from the airport.