Do the major networks air prime time programming over a live feed to all affiliates? Or are the non-live prime time shows taped earlier by each affilitate and played back later during prime time?

It depends on the show. Most are live feed now but I know one of my friends has an actual satellite dish (not a dss) but a big one and he used to get the Sunday Simpsons on Friday while Gracie films was beaming it to Fox for Sunday play.