Tripod
Can somebody confirm that both inputs left and right should both be working in stereo to begin with?
Both of those inputs are mono, so there's no way way to feed in stereo signal using only one of them. It's only the track FX that produces stereo that can give you stereo image. To record stereo you need to record left/right channel through the respective inputs.
If you record on a stereo track using left input, you get a stereo track with audio on the left channel only, and vice versa.
I don't know Quad Capture, and I could not find any answer in the specs on Rolands site concerning possible "special nature" of those inputs. In ALL interfaces I've seen in 20 years the combo inputs have been mono-only. That should be covered in the manual.
What kind of a plug is it that comes from guitar rig to Quad? Could it be that selecting "Stereo 1-2" combines the inputs to a fake stereo, feeding the "input 1" signal to both input channels? Just guessing...
Concerning your other question: The function is called Punch in-recording.