How is it a natural monopoly? A natural monopoly is something like the electrical poles and wires. I can't see how Uber could even become a normal monopoly even if everything went their way.

In most of their cities they are already a monopoly or near monopoly. Liquidity is a hugely massive advantage for both drivers and riders.

Both riders and drivers can use multiple apps without too much hassle.

Both buyers and sellers of second-hand goods can use multiple auction websites without much hassle, yet eBay still has a natural monopoly due to network effects. I doubt the network effect for uber is as strong as ebay, but I wouldnt completely dismiss it either.

Exactly. If you know a competitor can provide the equivalent service quality, but at significantly lower price, then users will switch. In a small market it is not too hard to let potential users know you exist and install your app.