SA definitely are integrated into the website for revenue bookings. I'm not sure why they don't appear on a EWR-LHR-CPT search, they appear if you search for JNB as the destination.

BA are shown as they are a valid carrier on this fare, as per the fare rules. You can confirm this on ITA, etc.

The CO website does not prioritise by alliance - it appears that it will by default show the flights in order of best fare and then connection time.