Sure they do. Not in bulk quantities, they take their profits on trading the spread. A lot of trades that they generally only make about a cent per share on each trade.

Market makers have their place, and you wouldnt have the liquidity you'd like if they weren't there. Market makers face relatively low risk as they dont generally hold positions for long, but they can also face severe penalties if theyre supposed to be in the market, but are not. My first boss was fired over a potential $600K USD fine because he took us out of the Options market (as a market maker) for an hour (potential fine was $10K/minute) and refused to accept accountability for his actions.

Also, trades are typically matched on a first in, first out basis with price/time priority. Market makers respond to messages that are essentially a request for liquidity if an appropriate contra order is not sitting on the exchange's order book.

Who gets paid commissions depends on what type of entity is on the other side of the trade and what agreements are in place with the meriad of counterparties involved (e.g. if you want to buy 10K shares of a company, that could be broken into, say, 20 trades of various quantities and prices below a limit until the quantity is fulfilled).