Brakes On a 2000 V-6

[blue00gt]

Yes, you should always downshift before the corner to keep the revs in the sweet spot. This serves to keep you in the powerband coming out of the corner and also makes throttle adjustments for correction more effective. I heel-and-toe downshift while I am braking coming into a corner.
You are definitely on the right track about using throttle adjustments to make corrections during the turn rather than moving the steering wheel. This is based on the fact that friction force is a constant multiplied by the weight pushing down on the tires. When you transfer the weight to the right tires, you are increasing the cornering load they can withstand without slipping.
Using the wheel to correct can be a very bad habit because a lot of people get away with it for awhile as they are not turning as fast as the car is capable of and have a little more traction left for turning when they turn the wheel more, but when you are cornering at the limit if you need to turn in more and try to use the wheel you are going to crash; letting off the gas transfers the weight to the front for better turning traction at the front wheels and the car will turn more without having to move the steering wheel. (Of course when you are deep in the throttle and hanging the car's booty out sideways or getting too out of control you will have to counter with the wheel also; I'm just talking about taking the proper line here rather than drifting).
You can practice weight transfer without even going very fast. You can feel the difference in how the car tries to turn at the same speed with the suspension properly loaded going into the corner compared to if you don't use the brakes and just turn the wheel.
Also, they key to driving fast is being smooth with all your input so as not to upset the chassis and tires. I stroke my gas pedal coming out of the corners like I stroke my women - nice and smooth.