Autocross a few times and you'll be able to answer all of those questions. It all depends on the type of corner and what follows the corner; sometimes you may not want to be in a lower gear because you'll run out of revs before you can grab the next gear (bouncing off the limiter during the exit is not ideal ;-).I've also come to understand that the most beneficial tool would be to do some autocross to help me learn the car's limits, and will be doing some at the first opportunity I get. But any thoughts in the meantime are appreciated.
When you first start to autocross, you'll shift into 2nd and leave it there. However, once you get quicker, you'll learn when and where to downshift. Depending on the lot you're running, sometimes 1st gear can handle the whole course (if you're a smooth driver).
Obviously you shouldn't practice any aggressive driving on the street (blah blah blah). A quick look around this forum can show what can become of your car if you drive like a jackass on public roads.