Yes, the 16R is an 18x18 USB recording interface. Studio One has a template for this mixer, so you can pretty fast be ready for recording. For using UC Surface and Studio One Remote you need a router. Remember to always let the router boot fully before you start the mixer. UC Surface on a laptop does NOT need the wireless network. I works via USB.
Faderport is a controller for Studio One, not the StudioLive mixers. I suppose you can use them as a tandem, but interface is interface and DAW is DAW. The rack mixers have no DAW mode like the consoles have. That really is the next step in bringing both worlds together.