And it's the USB connection that you're using to connect to the PC, rather than via another interface? As far as I can make out, the only way to set the output levels involves the controls on the mixer itself. Ideally you need a tone generator to apply to an input to see what the level recorded by Audition is when the meters say 0dB. Assuming this mixer works like most mixers do, then you don't want this signal to be anything like 0dB when it's recorded by Audition, as that would allow no headroom whatsoever. The metering appears to say that the clip light will come on at +8dB, and even that you want to be a little lower than 0dB as indicated on Audition's meters.
What that means in practice is that when the meter on the mixer says 0dB, you don't want this peaking at anything much over -10dB on Audition, and that would be pretty healthy. Running Audition at that level is fine; there's loads of dynamic range available and if you want to boost what's been recorded when you process it, that's fine - it won't be distorted just because somebody forgot to monitor the levels carefully enough... the chances are that in the Windows Mixer, there's a slider you can adjust to set this. It really is a lot easier to do with tone, though - if you're running several sets of this, then having a basic tone generator around is almost a must.
When I make live recordings, I always set the record level so that the loudest thing I know I have to record is at about -12dB, and that's always worked fine - there's 12dB for added enthusiasm!
Yes, USB cable comes out of the Air1 goes and into the HP Computer.