Perhaps the master volume level is just too loud in general? Also, do you race with the 'in game' engine sounds on or off?

Not so much trying to be cool as it is trying to be realistic. You won't see too many street legal cars with that effect, the race versions hower won't have any emissions control.

For now, if you want backfire, go play GTR or GT4

This also appeared in S1, and I think it has something to do with overlapping polygons? Perhaps they raise them up enough so they don't flicker as if they were on the same plane? I've seen it used in other games, but much less noticeable. I've gotten used to it recently and no longer notice.

This is not a bug unless your brake ratio when you did this was set to 100% Rear and 0% Front. The handbrake will add to the braking in the rear wheels because you do not have 100% full brake ratio in the rear for your normal brakes. Set the rear brake ratio to 100% and see if it continue to do it, if it does then yeah it's a problem.