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.
That said the fact it could happen it not really related to if it should happen - as you say it's unclear how much extra money would actually flow to drivers as potentially Uber is operating on thin margins.
2) The high liquidity of drivers would imply a functioning market (not to say that it's perfect). The most obvious solution for drivers who are unhappy with the pay would be to get a different driving job, right?
3) The core issue is that the barrier of entry to driving for Uber is very low, increasing labor competition. This also keeps the price of a ride low. The wage of the driver is the agreement between the rider and the driver for the service, Uber is acting as a mediator. There is nothing in this article that comes close to proving that Uber is not fulfilling it's role as a mediator.
4) It will be interesting to see if the app works, but the strategy seems flawed. The constrained variable are the riders; there are already plenty of options. Paying drivers more doesn't seem to be a very compelling reason for riders to choose a different service.