HFT firms are apparently hooked up directly to the exchange. So they probably settle trades in real-time. The whole chain of retail to broker to clearinghouse is what creates the need of credit-collateral at every stage and create systemic risk if some players don't have the right risk control in place. At least that's what I have figured from a few hours of reading.
They do not. They settle trades in 2 business days like everyone else. Think about it: if you sell a share to a HFT, how could the HFT receive it immediately when you don't need to deliver it for two days?
However there is a process called CNS (Continuous Net Settlement) which means you generally only have to settle the net of your trades each day.