These market place ideas don't work nearly as well for businesses where there are long term, repeated, interactions between seller and purchaser. They work best when there is a one time exchange, because a market is really getting paid to make an introduction.
edit: I see now that many people made this argument much more eloquently in other comments on this thread.
The 20% cut also does sound rather extreme, but if you build a very good product where you can end up charging even more than the usual price, the 20% isn't taken away completely from the supplier, and might end up more like a 10% actual cut.
Once the platform has a significant number of suppliers, sure. If the platform is new then attracting suppliers is the number one problem to solve, and that's really hard if it's too expensive.
That makes no sense. Why would/should instructors+students continue to give them 20% commission for follow-up classes beyond the first one? It seems like just wishful thinking. The app store situation is very unusual (monopoly/monopsony), and does not apply in this context.