Speaking as an instructor, there is a decidedly good chance that the "stay off the curbs" and "brake in a straight line" bits were organization mandated. I instruct with several organizations, and they all have different approaches to what we should and should not be teaching our students. As a rule of thumb, hitting the curbs and trail-braking will upset the car, and when you're in the right seat with a guy you just met, with uncertain car-control skills, an upset car is the last thing you want. I usually do it that way too, until I get a feel for whether the driver and car can handle those types of maneuvers. Now, if I was doing private instruction, with a repeat student, then it's a whole different deal, with different goals.
Street tires? With any R-comp or even hot street rubber, you should easily be able to break 1.0G in the corners, without being on the edge. Also, slow corner, fast corner, they're all the same, as long as you stay within your grip budget. The main difference is how far you slide when you push past the envelope. Your main objective, though was a good one!
