You can use Studio One with plugins when mixer and computer are connected via Firewire 400. By default there is a 1:1 routing, which means that channel 1 sends audio to track one for processing and track 1 sends the processed audio back to channel 1. If you will, you're "inserting" Studio One as processing and recording instance. You can also use buses in Studio One and send the processed sum back to the mixer. Check the manual for more einformation. There are also videos available.
The "old" Firewire and the "classic" mixers use former versions of software (UC Control, Studio One, Capture). If your computer does not have the old features and fits to the mixer, it's not guaranteed that you get everything running.