My understanding is that very few places have a medallion system. It's apparently quite common in the US, but I can't say I've heard about it anywhere else.
I don't know, and it's likely they don't do it at all.
Why would the number of taxis need to be controlled? I don't know much about the taxi industry and perhaps there is some good reason for it that I am simply not aware of?
My baseless assumption always has been that it is for two reasons:
* It's one of those situations where the free market fails. Because anyone with a car can give someone a ride, it creates a race to the bottom and nobody can make money. You'll note that one criticism of Uber is that they create exactly that situation.
* Safety and fraud prevention for customers
Note that the community has an interest in quality transportation, including for tourists.
But does controlling the number of taxis achieve those goals? The countries that I have experience with all have regulations attempting to ensure those very things that you mentioned, but none of them actively limits the number of taxis.
Does anyone have statistics on this?