Burnout: yes, with VDC off, you can slip the wheels pretty good. I haven't tried to sustain a real burnout though, because it's pointless and abusive.
Neutral: The paddle/stick up/down shifters don't have a way to reach neutral, but you can flip the stick from M to D to N to reach neutral. I typically do this as I'm coming down to a full stop.
Paddles while in D-mode: As noted above, roughly 5 seconds if you're cruising. It seems to stay in the selected gear longer if you stay at non-negligible torque levels (accel or decel hard). If you really want to stay, you can just flip the stick to M at any time anyways.
Also, if you've been cruising in D and flip the stick over to M, it has a tendency to downshift a bit automatically (I guess they're anticipating that you didn't flip it over just to cruise). Cruising at mild highway speeds in D mode in 7th for instance, when you flip to M it will drop to 5. There's a workaround for this if you want to take over the shifting without it downshifting uneccessarily in the process: First click the upshift paddle on the steering wheel, which puts it in temporary manual mode and stays in 7 (the gear you were already in), then flip the level over to M and it remains in 7.
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