The transaction fees large players pay are negotiated to nothing. The exchanges want liquidity, especially in the derivatives markets. HFT does provide a ton of that, so they can negotiate away the transaction fees (in exchange to agreeing to maintain some minimum volume.
Yep. Most large market makers enter into obligations with exchanges to make markets in a wide spectrum of funds. Even those which are not that profitable. In exchange, the market maker gets much lower fees.
Minor point, but actual market makers are required by law to make markets. In fact, the market makers basically are the exchange.
This is different from hedge funds which act as market makers by earning rebates by providing liquidity. These guys (and gals) are have no regulatory requirements to make markets.
