Since the exchange functions as a market maker, do they also make money on the spread ? Or is the Ask and Bid an exact match ? Maybe there is no way to know for certain without two accounts.

Also do you trade on multiple exchanges to perform inter-exchange arbitrage or for some other reason ?

> Since the exchange functions as a market maker, do they also make money on the spread ?

Market makers take a spread. They provide liquidity at a cost.

GDAX, for example, has a maker/taker type of fee structure that charges you based on your account volume: https://www.gdax.com/fees

There are many ways an exchange can collect fees. An exchange doesn't have to take a spread but it is too tempting since it is easily hidden.