> I don't see how an exchange is making money unless it charges ++% pr. transaction
As far as I know, they all do. An exchange's users foot the bill (plus a premium) for on-chain transaction fees if they want to withdraw their coins to a private wallet. But not only that, the real money is in fees for trading coins on the exchange. You slap a little bitty 0.25% fee on every trade, and all of a sudden the jillions of day-traders trying to make money swapping BTC for DOGE or whatever other altcoin-of-the-day and back are a firehose of cash. Those trades are just taking place in your database, not on-chain, so your costs for servicing them are tiny.
Running an exchange should be like running a casino: a license to print money. Of course, stealing all the money on the table at once is tempting too...