All of your questions will be resolved if you understand one key fact: "Exchanges are companies". If you want to know why they are not government entities, imagine the GOP backlash if they tried to own and run an exchange (I'm not sure how democrats would respond, but republicans would definitely cry wolf). They are businesses, which is why:
- market access and data will not be openly available at a reasonable price (you have to spend extra money if you want to redistribute the data). Yes, this is a profit center for the exchanges
- Exchange seats will be limited and cost money (profit center)
- Colocation will always cost money (people are willing to pay to colocate)
As far as DMMs are concerned, there is a legal obligation to place orders and offer a buy and sell price. More specifically, they are required to be at the inside bid or offer (buying at the best buy or selling at the best sell price) most of the time. This ensures that there's a reasonable counterparty when some other trader wants to buy or sell. There is some economic incentive to be a DMM, but they provide a real service to the markets.
A few example exchange companies that list on public exchanges:
NDAQ: NASDAQ OMX Group lists
NYX: NYSE Euronext
CME: CME Group (Chicago Mercantile Exchange)