Unfortunately the car really doesn't make a lot of exterior sound with the stock exhaust. I took the videos from a fair distance away with a zoom lens, so what little exhaust sound it makes is very faint in the video. The track is also part of an airport facility, so the planes cover up a lot, too. It sounds amazing from inside the cabin, though. I'm working on an exhaust upgrade - I've found the one I want, just have to buy it and get it installed.
This one is too far away to hear any sound from the car, but shows a bit of 1st-2nd shift wheelspin and the resultant tire smoke at about 9 seconds.
It's very possible. The outside tires were very loaded on those hard corners, and I had the car in Sport Mode (traction control off, but not totally defeated so I wouldn't spin out). The E-diff can only do so much, I imagine. I couldn't feel it spinning, though.