2) Yes, to a company that is owned by the drivers and gives them back the maximal share of the revenue, taking into account the (minimal) operating costs.
3) To call Uber a "mediator" when both the customer and the driver have no say in the cost of the fare is laughable. Uber unilaterally sets the price, and if you don't like it, you're shit out of luck.
4) Like the point I made in 1), Uber takes a much larger cut than what is truly necessary. Even if the hypothetical ridesharing co-op had the exact same fares as Uber, a much larger proportion of the fare goes to the driver. And I would disagree that riders are the only constrained variable - there is almost zero switching cost between different ridesharing services for not only the rider but the driver as well. If only Uber and the ridesharing co-op are the only options for ridesharing in a given city, and they have the exact same fares for customers, but the co-op pays the drivers better than Uber, any driver would logically switch to the co-op since they would be paid more, and the customers would quickly switch to using the co-op's app as well, since the waiting times would be shorter compared to Uber.