Although there are numerous public transport options in Johannesburg, it's definitely worth getting a car when livning in the city. There are numerous safety and reliability concerns regarding South African public transport. Minibus taxis are aplenty on the streets of Joburg, but taxi drivers generally ignore the rules of the road and a ride in these vans can be quite an experience, so prepare yourself for a lightning fast and scary trip. There are also buses along all the major routes in the city, but these are not always reliable. The best option for any expat is to buy or rent a car while in Joburg - just factor in traffic and petrol prices - as traffic can be quite nightmare in Joburg and you need to know and plan your route beforehand as Joburg drivers are not the most patient and like to drive fast. Check out Buying a Car in South Africa for more details on what you need to know about purchasing a vehicle in Johannesburg.
Hi there - private schools typically give out bursaries for disadvantaged children but I have never heard of this going to any expat children, this is reserved for South Africans of disadvantaged economic backgrounds. There are usually also scholarships available for high school (starting grade 8), your child would have to do a scholarship exam during their grade 7 year at the school of choice and see if they qualify. Scholarships are available for academics, sports, and sometimes music, and range from 25% to full tuition. However, there are only a few slots available at the schools that offer them (I know Dainfern College in Joburg does, and I assume the other private schools do too) so this is not something easily attained. Good luck!
I've got a lengthy post on my blog about "Tips on buying a car in South Africa" if you're interested in more info. Hope this helps!